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Use a graph and/or level curves to estimate the localmaximum and minimum values and saddle point(s) of thefunction. Then use calculus to find these values precisely...

Question

Use a graph and/or level curves to estimate the localmaximum and minimum values and saddle point(s) of thefunction. Then use calculus to find these values precisely.$$f(x, y)=x y e^{-x^{2}-y^{2}}$$

Use a graph and/or level curves to estimate the local maximum and minimum values and saddle point(s) of the function. Then use calculus to find these values precisely. $$f(x, y)=x y e^{-x^{2}-y^{2}}$$



Answers

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function.

$ f(x, y) = x^2 + xy + y^2 + y $

The problem is, find the local maximum and minimum values and societal point of the function. If you have three dimensional graphing software, graph the function with Dwayne and will point that review out the important aspects of the function for dysfunction. First compute Partial derivative affects of why FX is ego to why minus two minus two x I fly. I had to go to x one is 21 is 21 large FX is equal to 01 is equal to zero south. These two equations we have X. You see how to negative two y is equal to negative two. This function has one critical point negative to negative two. Then we compute second partial derivatives of XX f X Y. And that's why why F x X is equal to two. F x y is equal to one. If my wife is able to negative two. The D is equal to four minus one. It's going to that zero. Have X X is equal to negative. Two is less than zero. So negative two Negative two uh, negative to negative two is a local maximum. Now look at a graph of this function so we can see dysfunction disappointed, negative to negative tool. The function has a local maximum

The problem is finding the local makes maximum on minimal wells on the center point of the function. If you have three dimensional, graphing, fluffier rough, the function with the Dominion will point that reveal out important aspects of the function. So first they would compute partial after flax. This is the culture to Max plus two R. I should have a party. Why is he called you four times last cue plus two ax at the possible. Some. Are you called to zero? So from Christian wanted behalf actually connect your why flying to the equation to a half onlys cube. While this to live, it's equal zero. So like to see what you're Cyril, or why it is a good person minus one over square root of two. So we'LL have three critical points. Zero zero one over square root of two negative one over square root of two one negative one over square root of to one hundred square it, too. I'm a computed thanking a partial derivatives, a fact sex is equal to two x, y and z. What, too, After, why? Why, you see go to twelve times last square. That is a point of zero zero we have. Why Why is he going to serial B? It's like a connective war. It's the last thing. Zero zero zero is a side of point that is point one over a sky. Courage of too negative, one of discarded, too. And it's a point next one hour, discarded, too. One always square into two. Why, why it's equal to six. Thirteen. Is the country twelve minus forces? This is it, Richard. And zero. A fax sex is going to choose off greater than zero this two points. Local minimal. Now look at this graph for dysfunction from the graft. Off this function, we can see that was the point one that worry square root of two negative one that was square root of two and negative. Well, now with the square root of two, when I was scared, too. The function has the local minimum value, but that is a point of zero zero and his nether local maximum, nor look minimum

So problem is finding the local maximum and minimum values and stead of points after function. If you have three dimensional graphing some fire ralph the function without the one you will point to reveal without important as acts with the function A fax Why's he wanted to minus X to the power for prostitute exploit from minus y Score the first two computer pasha laugh tracks But this is you got Connective ward have sacks cube as wax Pasha Pasha, Why is he going to know why? So the light possible? Some cereal we have Why is he put the Cyril access? He got your zero plus or minus one. So we have three critical points. Zero zero one zero ninety one zero. Then we compute second positive relative A fact sex is he got you Negative twelve X square US or X Y z zero Why wide secret connected to So I'm disappointed. Zero zero off expects or so there is a god or perhaps next year, too. My Cyril's This's connected it. It's the last time. Zero zero zero is a sign of point. That is point one zero that is appointed next one zero. We have sex. It's got negative, right? It's like zero deed is equal to sixteen piss bridges and zero it is. Two points are no call. Maximo. Now look at its glove with the function from the graph. Shows up dysfunctional can say at this point one zero and make two one zero function cars, a local maximum value. My task is a point of zero zero. It is a matter for the local maximum maximum nor local minimum.

The problem is finding the local maximum minimum while eels saddle point of the function. If you have three dimensional graphing southwire rough the function with divine way point that reveal out important aspect of the function. The first to be computed a fax. Relax. This is a good all schools. So cube once forks on the part of puss y three y squared minus three life possibles on you called zero we have X is equal to zero plus or minus one. Why his secret? You? That's all minus one. There's a fortune Have six critical points. Also, my won won. That's minus one next to one zero one zero ninety one. Then we compute second part of derivatives Fox. Lex, it's the court. Your twelve exploiter minus four. Why? Why? And so you want to six. Why? And slide here too. Zero Then after the point, us minus one one. That it is two points off xx. And so you could chew, right? Why? Why is equal to six the Is that you? What is eight its greatest. And Cyril, a seance. Axe axe is also gritted at zero. It is two points are local, minimal at this point possum minus one on detective one axe axe is we got to it. Why? Why? It's the connective six that is a negative or debate is less than zero. They are sent off once at this point zero one we have off XX. It's the culture. Thank you for half. Why? Why it's because of you. Six. Thirty Is the culture negative? Twenty four It's last time. Zero. It is a side of point At this point zero ninety one fxx is equal to nectar for a while. Why it's connective six. The culture before its security is at zero. Things affects X is less than zero. It is a no calm maximum. Now let's look at this a graph of the function so we can see it is a point these two points that they have to local minimum on Dhere one local maximum So apostle minus one Next one well plus minus one one local minimum for here. Local minimum on DH zero next to one of the local maximum mother. Three points. They are later local maximum nor local minimum, So there are seven points


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