How to of the Day

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• How to Find Extrema of Multivariable Functions
• How to Do Center Splits
• How to Build Love With Your Bearded Dragon

How to Find Extrema of Multivariable Functions Posted: 15 Sep 2016 05:00 PM PDT In single-variable calculus, finding the extrema of a function is quite easy. You simply set the derivative to 0 to find critical points, and use the second derivative test to judge whether those points are maxima or minima. When we are working with closed domains, we must also check the boundaries for possible global maxima and minima. Since we are dealing with more than one variable in multivariable calculus, we need to figure out a way to generalize this idea. EditSteps Consider the function below. ${\displaystyle f}$ is a twice-differentiable function of two variables ${\displaystyle x}$ and ${\displaystyle y.}$ In this article, we wish to find the maximum and minimum values of ${\displaystyle f}$ on the domain ${\displaystyle |x|\leq 1,\ |y|\leq 2.}$ This is a rectangular domain where the boundaries are inclusive to the domain. ${\displaystyle f(x,y)=x^{3}+x^{2}y-2y^{3}+6y}$ Calculate the gradient of ${\displaystyle f}$ and set each component to 0. Recall that in two dimensions, the gradient ${\displaystyle \nabla f=\left({\frac {\partial f}{\partial x}},{\frac {\partial f}{\partial y}}\right).}$ ${\displaystyle {\frac {\partial f}{\partial x}}=3x^{2}+2xy=0}$ ${\displaystyle {\frac {\partial f}{\partial y}}=x^{2}-6y^{2}+6=0}$ Solve for ${\displaystyle x}$ and ${\displaystyle y}$ to obtain the critical points. Generally, we will need to work with both components of the gradient to do this. Let's start with the first component to find values of ${\displaystyle x.}$ We can immediately factor out an ${\displaystyle x,}$ which gets us ${\displaystyle x=0.}$ The quantity in parentheses can also be 0, but that only gets ${\displaystyle x}$ in terms of ${\displaystyle y.}$ ${\displaystyle {\begin{aligned}3x^{2}+2xy&=0\\x(3x+2y)&=0\\x&=0\end{aligned}}}$ ${\displaystyle {\begin{aligned}3&x+2y=0\\&x=-{\frac {2}{3}}y\end{aligned}}}$ Next, we move to the second component to find corresponding values of ${\displaystyle y}$ for the two values of ${\displaystyle x.}$ ${\displaystyle x=0:}$ ${\displaystyle {\begin{aligned}6&=6y^{2}\\y&=\pm 1\end{aligned}}}$ ${\displaystyle x=-{\frac {2}{3}}y:}$ ${\displaystyle {\begin{aligned}{\frac {4}{9}}y^{2}-6y^{2}+6&=0\\\left(6-{\frac {4}{9}}\right)y^{2}&=6\\y^{2}&={\frac {27}{25}}\\y&=\pm {\frac {3{\sqrt {3}}}{5}}\end{aligned}}}$ We've found all possible values for ${\displaystyle y.}$ Substituting ${\displaystyle y}$ only for the values that we got using the relation ${\displaystyle x=-{\frac {2}{3}}y,}$ we obtain ${\displaystyle x=\mp {\frac {2{\sqrt {3}}}{5}}}$ (note the signs). Therefore, the four critical points are ${\displaystyle (0,\pm 1),\ \left(\mp {\frac {2{\sqrt {3}}}{5}},\pm {\frac {3{\sqrt {3}}}{5}}\right).}$ These are only candidates for extrema, however. Use the Hessian matrix to determine the characteristics of the critical points. This matrix is a square matrix of second derivatives. In two dimensions, the matrix is as below. ${\displaystyle H={\begin{pmatrix}{\dfrac {\partial ^{2}f}{\partial x^{2}}}&{\dfrac {\partial ^{2}f}{\partial x\partial y}}\\{\dfrac {\partial ^{2}f}{\partial y\partial x}}&{\dfrac {\partial ^{2}f}{\partial y^{2}}}\end{pmatrix}}}$ Calculate second partial derivatives of ${\displaystyle f}$ and substitute the results into ${\displaystyle H}$. Note that Clairaut's theorem guarantees that mixed partials commute (for continuous functions), so in two dimensions, the off-diagonal elements of the Hessian are the same. See the tips for another reason why this must be true. ${\displaystyle {\frac {\partial ^{2}f}{\partial x^{2}}}=6x+2y}$ ${\displaystyle {\frac {\partial ^{2}f}{\partial x\partial y}}={\frac {\partial ^{2}f}{\partial y\partial x}}=2x}$ ${\displaystyle {\frac {\partial ^{2}f}{\partial y^{2}}}=-12y}$ ${\displaystyle H={\begin{pmatrix}6x+2y&2x\\2x&-12y\end{pmatrix}}}$ Check the determinant of ${\displaystyle H}$. If ${\displaystyle \det H>0}$ (positive definite), then the point is either a maximum or a minimum. From an intuitive perspective, second partial derivatives of both components have the same sign. On the other hand, if ${\displaystyle \det H<0}$ (negative definite), then the point is a saddle. Second partial derivatives of the components have opposite signs, so the point is not an extremum. Finally, if ${\displaystyle \det H=0}$ (indefinite), then the second derivative test is inconclusive, and the point could be any of the three. See the tips for why this is the case. Let's substitute in the ${\displaystyle (0,\pm 1)}$ critical points. Since we are only interested in the sign of the determinant, and not the values of the elements themselves, we can clearly see that both points results in a negative determinant. This means that ${\displaystyle (0,\pm 1)}$ are both saddle points. We do not need to go further for these two points. ${\displaystyle {\begin{vmatrix}\pm 2&0\\0&\mp 12\end{vmatrix}}<0}$ Now let's check the ${\displaystyle \left(\mp {\frac {2{\sqrt {3}}}{5}},\pm {\frac {3{\sqrt {3}}}{5}}\right)}$ points. ${\displaystyle {\begin{aligned}{\begin{vmatrix}-{\frac {6{\sqrt {3}}}{5}}&-{\frac {4{\sqrt {3}}}{5}}\\-{\frac {4{\sqrt {3}}}{5}}&-{\frac {36{\sqrt {3}}}{5}}\end{vmatrix}}&={\frac {\sqrt {3}}{5}}(216-16)\\&>0\end{aligned}}}$ ${\displaystyle {\begin{aligned}{\begin{vmatrix}{\frac {6{\sqrt {3}}}{5}}&{\frac {4{\sqrt {3}}}{5}}\\{\frac {4{\sqrt {3}}}{5}}&{\frac {36{\sqrt {3}}}{5}}\end{vmatrix}}&={\frac {\sqrt {3}}{5}}(216-16)\\&>0\end{aligned}}}$ Both of these points have positive Hessians. Check the trace of ${\displaystyle H}$. For candidate extrema, we still have to figure out whether the points are maxima or minima. In that case, we check the trace - the sum of the diagonal elements of ${\displaystyle H}$. If ${\displaystyle \operatorname {tr} H>0,}$ then the point is a local minimum. If ${\displaystyle \operatorname {tr} H<0,}$ then the point is a local maximum. From above, we can clearly see that ${\displaystyle \operatorname {tr} H\left(-{\frac {2{\sqrt {3}}}{5}},{\frac {3{\sqrt {3}}}{5}}\right)<0,}$ and therefore, ${\displaystyle \left(-{\frac {2{\sqrt {3}}}{5}},{\frac {3{\sqrt {3}}}{5}}\right)}$ is a local maximum. Similarly, ${\displaystyle \operatorname {tr} H\left({\frac {2{\sqrt {3}}}{5}},-{\frac {3{\sqrt {3}}}{5}}\right)>0,}$ so ${\displaystyle \left({\frac {2{\sqrt {3}}}{5}},-{\frac {3{\sqrt {3}}}{5}}\right)}$ is a local minimum. Check the boundaries if you are finding extrema in a closed domain. For open domains, this step is not needed. However, since our domain is closed, extrema can occur on the boundaries. Although this becomes a single-variable extrema test, it is a tedious process for even the simplest type of domain - a rectangular domain - and for more complex domains, it can get quite complicated. The reason is because we need to take four derivatives corresponding to each side of the rectangle, set all of them to 0, and solve for variables. Let's check the right side of the rectangle first, corresponding to ${\displaystyle (1,y).}$ ${\displaystyle {\begin{aligned}f(1,y)&=-2y^{3}+7y+1\\{\frac {{\mathrm {d} }f}{{\mathrm {d} }y}}&=-6y^{2}+7=0\end{aligned}}}$ ${\displaystyle y=\pm {\sqrt {\frac {7}{6}}}}$ The critical points are therefore ${\displaystyle \left(1,\pm {\sqrt {\frac {7}{6}}}\right).}$ Doing single-variable second derivative tests on both of these points, we find that ${\displaystyle \left(1,{\sqrt {\frac {7}{6}}}\right)}$ is a local maximum and ${\displaystyle \left(1,-{\sqrt {\frac {7}{6}}}\right)}$ is a local minimum. The other three sides are done in the same fashion. In doing so, we net the critical points below. Beware that you must discard all points found outside the domain. ${\displaystyle (0,2),}$ local minimum ${\displaystyle \left(-1,{\sqrt {\frac {7}{6}}}\right),}$ local maximum ${\displaystyle \left(-1,-{\sqrt {\frac {7}{6}}}\right),}$ local minimum ${\displaystyle (0,-2),}$ local maximum Check the corners if you are finding global extrema in a closed domain. The four corners of the rectangular boundary must also be considered, just as how the two endpoints of a domain in single-variable calculus must be considered. Every extrema inside the domain and on the boundary of the domain, with the addition of the four corners, must be plugged into the function to determine global extrema. Below, we list the locations of the global maximum and minimum. They have values of ${\displaystyle f\approx \pm 6.041,}$ respectively. Notice that neither of these global extrema were located inside the domain, but on the boundaries, which demonstrates the importance of identifying closed vs. open domains. Global maximum: ${\displaystyle \left(1,{\sqrt {\frac {7}{6}}}\right)}$ Global minimum: ${\displaystyle \left(-1,-{\sqrt {\frac {7}{6}}}\right)}$ Above is a visualization of the function that we were working with. We can clearly see the locations of the saddle points and the global extrema labeled in red, as well as the critical points inside the domain and on the boundaries. EditTips It is a good idea to use a computer algebra system like Mathematica to check your answers, as these problems, especially in three or more dimensions, can get a bit tedious. In step 5, we said that for continuous functions, the off-diagonal elements of the Hessian matrix must be the same. Not only is this shown from a calculus perspective via Clairaut's theorem, but it is also shown from a linear algebra perspective. The Hessian is a Hermitian matrix - when dealing with real numbers, it is its own transpose. An important property of Hermitian matrices is that its eigenvalues must always be real. The eigenvectors of the Hessian are geometrically significant and tell us the direction of greatest and least curvature, while the eigenvalues associated with those eigenvectors are the magnitude of those curvatures. As such, the eigenvalues must be real for the geometrical perspective to have any meaning. When finding the properties of the critical points using the Hessian, we are really looking for the signage of the eigenvalues, since the product of the eigenvalues is the determinant and the sum of the eigenvalues is the trace. Oftentimes, problems like these will be simplified such that the off-diagonal elements are 0. Conducting the second partial derivative test will therefore be easier and clearer. In step 6, we said that if the determinant of the Hessian is 0, then the second partial derivative test is inconclusive. The reason why this is the case is because this test involves an approximation of the function with a second-order Taylor polynomial for any ${\displaystyle (x,y)}$ sufficiently close enough to ${\displaystyle (x_{0},y_{0}).}$ This polynomial can be written in a quadratic form as below, where the matrix in the middle is the Hessian. Higher-order approximations must be used if the second partial derivative test is inconclusive, just like in single-variable calculus. ${\displaystyle {\frac {1}{2}}{\begin{pmatrix}x-x_{0}&y-y_{0}\end{pmatrix}}{\begin{pmatrix}{\dfrac {\partial ^{2}f}{\partial x^{2}}}&{\dfrac {\partial ^{2}f}{\partial x\partial y}}\\{\dfrac {\partial ^{2}f}{\partial y\partial x}}&{\dfrac {\partial ^{2}f}{\partial y^{2}}}\end{pmatrix}}{\begin{pmatrix}x-x_{0}\\y-y_{0}\end{pmatrix}}}$ Expanding out the quadratic form gives the two-dimensional generalization of the second-order Taylor polynomial for a single-variable function.

How to Do Center Splits Posted: 15 Sep 2016 09:00 AM PDT The center splits is one of most impressive ways to showcase your flexibility. It involves extending the legs in opposite directions until they form a 180 degree angle, which is useful in array of physical activities, including gymnastics, martial arts and dance. The only way to achieve a complete center splits is through rigorous and repeated stretching. This article will show you some of the best exercises for increasing flexibility, along with some tips on how you can achieve center splits quickly and safely. EditSteps EditStretching Your Way to Splits Do a butterfly stretch. The butterfly stretch is a great stretch for the center splits as it increases flexibility in the inner thighs, the groin and the hips. To perform: Sit on the floor and bend your knees until the soles of your feet are touching. Pull your heels as close towards your body as possible and use your elbows to push your knees towards the floor. Make sure to sit upright with your back straight. Hold the stretch for 30 to 60 seconds. To deepen the stretch, lean forward as far as you can and place your hands on the floor in front of your feet. Keep your back straight and your knees pressed to the floor.[1] Do a pancake stretch. The pancake stretch is used by gymnasts to increase their flexibility and prepare for the center splits. To perform: Sit on the floor and spread your legs as wide as possible into a straddle position. Make sure that your legs are completely straight and that your toes are pointed. Keeping your back straight, lean forward as far as you can with your arms stretched out in front of you. Try to touch your chest to the floor, so your body is completely flat - just like a pancake! To deepen the stretch, try to grab your feet with your hands, while keeping the rest of your body flat to the ground. Hold the stretch for 30 seconds.[1] Touch your toes. Touching your toes stretches your leg muscles and increases flexibility in the hamstrings, which is great for center splits. This stretch can be performed in a seated or standing position. To perform the stretch while standing, stand with your feet together and your legs straight. Reach down and attempt to touch your toes with your fingertips. Don't bend your knees and try to place your weight on the balls of your feet, rather than your heels. Hold this stretch for 30 to 60 seconds. To perform the stretch while seated, sit with your legs stretched out straight in front of you and lean forward (keeping your back straight) until your touch your toes with your fingers. As you grow more flexible, try to grab the soles of your feet with your hands, in order to increase the stretch.[2] Do a bent knees stretch. This stretch increases flexibility in the groin and hips. If you can perform it correctly, you are well on your way to achieving center splits. Kneel on the floor and place your hands on the ground in front of you for balance. Move your knees outwards - as far from your body as possible - until they form 90 degree angles. There should be a straight line running from one knee to the other. Move your weight from your hands to your elbows, to get deeper into the stretch. The goal is to get your hips flat on the ground, while maintaining the 90 degree angle with your knees. Once you have achieved the correct position, hold this stretch for 30 seconds.[1] Do half squats. The half squat is a useful exercise for stretching the inner thighs. To perform: Hunker down into a low squatting position. Shift your weight onto your right leg and stretch your left leg straight out to the side, as if you were doing the center splits with that leg. Make sure to point your toes. Place your right hand on the floor (in front of your right leg) for balance and use your elbow to push the knees outwards until you feel a firm stretch in the inner thighs. Hold for 60 seconds, then repeat with the other leg.[3] Do standing leg stretches. These simple leg stretches are essential when training to do the splits, as they increase flexibility in all of the necessary muscles. They are commonly used in martial arts training as preparation for the center splits. To begin, stand up straight and place your feet two shoulder widths apart. Bend forwards at the hips, keeping your legs completely straight. Let your body hang down and try to place your palms on the ground. As flexibility increases, try to get your elbows on the ground. Hold this stretch for 30 seconds. Next your can try ankle grabs. Lean to the right and grab the right ankle with both hands, then lean to the left and repeat with the left ankle. When holding these stretches, make sure that your hips are level rather than tilted to the side, otherwise the stretch will not be as effective. Next, try grabbing both ankles at the same time, bringing your chest as close to your knees as possible. Keep your back straight and relax your neck muscles so that your head is hanging straight down. Practice your full center split. Of course, one of the best ways to achieve center splits is to practice doing center splits. The safest, most effective way to do this is as follows: Hunker down into a low squat and place both hands on the floor in front of you. Then, slowly begin to walk or slide both feet outwards, as far apart as you can manage. Your legs should be completely straight and your feet should be parallel as you lower yourself down into the stretch. Many people make the mistake of lowering themselves down by rolling back on their heels, but this will not provide as effective of a stretch and could cause injury. Your toes should only point outwards when you have achieved the full splits. Hold the stretch for as long as you can, then slowly come back into a squatting position to rest your muscles. When you feel ready, lower yourself back into the splits position again. Alternating between squatting and stretching will help you to get lower down each time you attempt the center splits. As you stretch, remember to keep your back straight and your hips in line with your legs. If your hips are too far forward or too far back, you will not be able to perform a center split correctly. The goal is to lower yourself down until your groin touches the floor. Once you have achieved this, you can try to roll your hips until you are sitting in an upright position, while maintaining a center splits. Remember to move slowly and breathe evenly. Do not push yourself too hard. You should feel a tight stretch in your inner thigh and groin muscles, but it should not feel painful. If you feel any discomfort or tearing sensations, come out of the stretch immediately. EditAchieving the Splits Quickly Yet Safely Always warm up before you stretch. It is essential that you warm up before you stretch, in order to avoid injury and maximize your natural flexibility. Try doing jumping jacks or running on the spot for a few minutes before you begin your stretching routine. Alternatively, do your stretching at the end of a cardio workout . You will get the double benefit of increasing your flexibility while preventing muscle stiffness after your workout. Stretch every day. Achieving the center splits requires a high level of flexibility, and flexibility is something that needs to be worked at consistently over time. In order to achieve the flexibility required for center splits, you need to be stretching every single day, or as close to it as possible.[4] Begin by stretching for 15 minutes a day, using a routine comprised of the stretching exercises outlined above. After a couple of weeks, increase the time spent stretching to 30 minutes a day, if possible. You can break this up into two 15 minute sessions a day. Remember that the more stretching you do, the faster you will achieve center splits. Enlist the help of a friend. When stretching for the center splits, it can be very useful to enlist the help of a friend. Your friend can help by observing your posture, which can be difficult to correct by yourself. Ask them to make sure that your hips are in line and your shoulders are even. This is important as poor posture can affect the quality of your stretching and even cause injuries. A friend can also help you to deepen your splits by pushing down lightly on your shoulders or legs as you stretch. This can help you to get a fraction or two deeper into your stretch than you could on your own. Just make sure that they will respond quickly if you ask them to stop. Wear socks. One simple tip that can help you to deepen your splits is to wear socks while you stretch, rather than stretching in your bare feet. The socks will allow your feet to slide easily along the ground, helping you to get deeper into the stretch. This is more effective on wooden floors than on carpet. However, make sure that you slide into the stretch in a careful and controlled fashion. Sliding too quickly may cause you to pull a muscle or tear ligaments. For safety, most of your body weight should be supported by your arms as you slide into a center split. Find a practice space that works for you. When working towards the center splits, it is important that you find a suitable environment for stretching and practice. The type of environment that works best for you will depend on personal preference. Some people prefer to practice their center splits in a quiet, peaceful environment. They consider their stretching routine to be a type of meditation, where they can clear their mind and focus only on the sensations of their body. Other people find stretching a chore and need something to entertain themselves as they go through their routine. For example, some people like to watch television to distract themselves as they stretch. Know your limits. The ability to perform the center splits is an impressive physical feat which requires discipline and perseverance to achieve. However, it is also important that you know your limits and refrain from pushing yourself past them in order to achieve your goal. Pushing yourself too hard will only result in injury, which could potentially prevent you from ever being able to do the splits. To safely yet effectively achieve the center splits, perform each stretch slowly and carefully, paying close attention to maintaining the correct posture. Listen to your body and you will soon achieve your goal! EditVideo EditTips Always breathe out (exhale) while going into a split, this will help you get farther into your split. Be Patient. If you are a beginner and you don't get it the first time, just keep on practicing. Remember that it takes months to accomplish this, not hours. You could also do wall splits. That is when you face the wall and stretch your legs out as if you we're going to do a split. Go as far as you can until you feel a stretch in your legs. EditWarnings Don't push yourself too far. This won't help your splits. It will make your splits worse due to leg injury. Be aware that some body types will never be able to achieve full center splits, no matter how much stretching they do. EditRelated wikiHows Do an Aerial Cartwheel Run up a Wall and Flip Do a Three Step (Gymnastics) Do a Front Handspring EditSources and Citations Videos provided by MalovaElena Cite error: <ref> tags exist, but no <references/> tag was found

How to Build Love With Your Bearded Dragon Posted: 15 Sep 2016 01:00 AM PDT When you own a bearded dragon, it is natural to want to love your pet. Your dragon also can have affection for you if you take care of him. Learn how to hold him appropriately, bathe, and house him. By providing a good and safe home for your pet, you show your love. EditSteps EditProviding a Good Home Purchase a high quality vivarium. A vivarium is a wooden tank with a glass front. It should have a tight lid and smooth sides to prevent the dragon from hurting his nose. Look for a vivarium that will be easy to clean. Vivariums should have a polyurethane or waterproof sealing. You should make sure the joints are caulked as well.[1] If you waterproof a vivarium yourself, be sure to allow the vivarium to dry for a week before putting your dragon in his home.[2] Make sure your dragon has enough space to run around, climb, and sit on branches.[3] Clean your pet's habitat thoroughly regularly with a 10:1 mixture of water to bleach.[4] Remove any vegetables that he does not eat within four hours. Remove uneaten insects at the day's end.[5] Use an aquarium. You can also purchase an aquarium for your dragon. Baby dragons can live in a 10-15 gallon aquarium, while adults need a larger 55-60 gallon space.[6] Aquariums are a better short-term solution because it is difficult to regulate the temperature in them.[7] Provide a vivarium and a heater. Wooden vivariums encapsulate heat better than glass or metal does. Aim to provide a less warm area (30 degrees Celsius/86 degrees Fahrenheit) and a warmer section (45 degrees Celsius/113 degrees Fahrenheit). The vivarium should be no smaller than 48 x 24 x 24 inches. Make sure your vivarium has air vents, minimally one per square foot. The vent should be on the upper part of the back wall rather than on the lower section.[8] See Care for Bearded Dragons for additional instructions on how to set up your pet's habitat and vivarium. You can purchase a vivarium or make your own using DIY kits, such as Vivexotic.[9] Install a good substrate. A substrate is the material that fills the bottom of the vivarium. Your pet will dig into the substrate.[10] Aim for a substrate that looks natural and makes your dragon feel at home. The substrate should also be absorbent. Because your dragon might eat parts of it unintentionally, try to find substrate that is non-toxic and safely digestible. You can utilize smooth newspapers, indoor or outdoor carpet, brown paper, or AstroTurf[11]. Do not use wood chips or shavings, gravel, cat litter, or soil with pesticides, vermiculite, fertilizers, or surfactants for your substrate[12] Provide appropriate furniture. Include branches for climbing. A reptile hammock is also fun for your pet and available at pet stores. Equip your dragon's space with a "reptile hide," which is an enclosed area in which your dragon can hide from you. Your dragon also will use this space for long periods of sleep. Place a "basking platform" in the habitat as well. This can be a rock or another surface within six to eight inches of the basking light source. Here a dragon can warm himself.[13] Be sure to strip all bark from natural wood branches so that your dragon does not eat the wood. Clean all branches prior to use.[14] EditHolding Your Bearded Dragon Know good practices. Dragons actually like to be held. Wait three to four days after the dragon's arrival to start holding him. Wash your hands before and after handling the pet. Begin by holding him for short periods multiple times a day. This helps build trust slowly. When holding your dragon, strive to have a quiet setting.[15] Babies, young children, women who are or might be pregnant, the elderly, or people with weakened immune systems should be careful about touching the dragon or being near its home.[16] Salmonella infections can occur.[17] Consult a doctor if you or your child belongs to one of these populations before allowing contact with the reptile. See Hold a Bearded Dragon for thorough tips. Pick up the dragon. Gather your dragon from underneath his body in a slow, yet self-assured, scooping motion. Support his whole body plus his legs and tail.[18] Do not hold or pull your dragon by his tail. It can come off![19] Calm your dragon. It is important to tame your dragon from the beginning. If your dragon appears aggressive (his "beard" will darken),[20] hold him tightly (not too tightly) with both of your hands and pet him. If your pet appears particularly agitated, release him for a short moment and then try holding him again until he calms himself. Training your dragon to be held and calm can take a number of months but it is vital to creating a good relationship with your dragon.[21] EditBonding With Your Dragon Through Care Feed your dragon by hand. One way to bond with your dragon is to give him his food directly. You should do this occasionally but not so often that your dragon becomes reliant upon you. Instinctually, dragons hunt for their food so you should still give your dragon his food in a bowl most of the time. Place the food on the tip of your fingers. Your dragon will use his tongue to take the food from you. [22] Bearded dragons eat vegetables, living insects like crickets, waxworms, or mealworms, or bearded dragon foods available for purchase at pet shops.[23] Safe vegetables include squash, endive, turnip greens, or collard greens. Dragons also can eat apples, strawberries, and melons.[24] Do not feed your pet spinach, avocado, lettuce, or wild insects.[25] Implement a regular feeding plan. Whether feeding by hand or putting the food in your dragon's home, your dragon will anticipate feeding time. He then will associate a positive experience with you![26] You should feed your young dragon once daily and your adults once per day or every second day.[27] Juvenile dragons require a mainly live food diet. Beardies are able to transition onto a vegetarian diet as they mature. It is possible your dragon might think your fingers are food. Be careful when feeding him![28] Bathe your bearded dragon. By giving your lizard a bath, you will help him stay hydrated. Dragons absorb water through their pores. This is particularly important because dragons do not love to drink form a water bowl. To bathe your dragon, fill a sink, bathtub, or other clean container with warm water (try to reach 34.5-35.5 degrees Celsius/94-96 degrees Fahrenheit). Your dragon might enjoy this activity and again associate pleasure with you![29] Be sure to clean the bathing container thoroughly after use.[30] Mist your pet with water every second day. This will help your lizard also to stay hydrated.[31] Try to bathe your pet every four to eight days although you can bathe him every day.[32] Aim for a stress-free environment. In order for your dragon to be happy, you should try to reduce his stress levels. High stress can lead to aggression. When your dragon sleeps, keep the noise levels in your house down. When your dragon decides to hide under something, this could signal that he wants to be alone. Try to respond appropriately to your dragon's behavior and avoid disturbances unless there is a pressing need.[33] It's okay to let your dragon roam a bit outside his habitat. Just be sure to keep him from the kitchen or other rooms where you eat or prepare food.[34] Take your dragon to the veterinarian. Like any pet, bearded dragons should have yearly check-ups. Also, if you sense that your bearded dragon is acting differently than normal, schedule an appointment with the vet. Mites are a common issue that dragons face--they suck the reptile's blood. Only a vet can determine, though, through testing whether your pet is truly ill.[35] EditRelated wikiHows Care for Bearded Dragons Look After Baby Bearded Dragons Teach a Bearded Dragon to Drink from a Water Bowl EditSources and Citations Cite error: <ref> tags exist, but no <references/> tag was found

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