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Find the loca Mazimum ang minlmum values and saddle polnt(s) the functlon If you have three-dlmensiona graphing software graph the function wlth nomaln aspects the ...

Question

Find the loca Mazimum ang minlmum values and saddle polnt(s) the functlon If you have three-dlmensiona graphing software graph the function wlth nomaln aspects the function. (Enter dns"erc commm separated list. Jns Ver does exist, enter DNE: ) fx,Y) 3+2 3y2vlewpolnt that reveathe Importantmayimum value(s)loca mnimmm valuesaddle point(s)(xy 0 --14 26). ( 3.01Meed Help?Koraaln

Find the loca Mazimum ang minlmum values and saddle polnt(s) the functlon If you have three-dlmensiona graphing software graph the function wlth nomaln aspects the function. (Enter dns"erc commm separated list. Jns Ver does exist, enter DNE: ) fx,Y) 3+2 3y2 vlewpolnt that revea the Important mayimum value(s) loca mnimmm value saddle point(s) (xy 0 - -14 26). ( 3.01 Meed Help? Koraaln



Answers

For the following exercises, determine the extreme values and the saddle points. Use a CAS to graph the function.
$$
f(x, y)=\sin (x) \sin (y), x \in(0,2 \pi), y \in(0,2 \pi)
$$

Everyone could I get going to solve a problem? Number five if with respect to X has given by So it's minus two equals zero if with respect to buy is going by two by minus six sequence zero. So to find the critical points, identify them as relate to extreme. A function of an ex con. Allah is given by X minus one the whole square plus y minus trita whole square and required them to zero. They get like executor one and why you kowtow. Three critical point is one comma three. So if double the transport access to have doubled derivative introspective ways to F X ways zero critical 0.1 comma three to decide whether it is related to maximum or minimum. So we can use d equals toe in their two minus zero square, which is full so days together than zero. Fxx is greater than zero, which means it is related minimal. Thank you

Today, we're going to solve a problem. Number 14 here F with respect Alexis two X minus three y equals zero. If we respect the ways minus tree, it's minus two way equals zero to find the critical points the function of because it's square minus three x way minus y squared and equipped them to zero. So three effects plus tau a fight equals minus 13. Right, which is a little Mexico zero Where you go. Zero critical points are zero comma zero. So now we need to calculate three effects. Plus to avoid to get rid off X if double that of it too, is if my wife is minus two. Have X ways minus street. Critical points is at zero comma, zero d equals toe and U minus two minus three whole square, which is minus study. So they less than zero. It is, sadly point zero comma zero. Thank you

Today we're going to start trouble number have with respect to exist towards plastics. Fight equals zero if with respect always 66 plus 21 minus four equals zero So functional vehicles pigs a squid plus six six way plus 10 white square minus four white blissful so three effects minus F y equals minus two y plus four equals zero eggs equals minus six. What equals critical points off minus six Come on. Three FX minus have like equals minus two white plus for because zero if x x equals two f y y equals 20. If picks make was six d equals to do 20 minus six square, which is four. These occurred that zero f x x is greater than zero related minimum.

Okay, so we're trying to find the minimum and maximum values for dysfunction here. So first we need to do when you take the derivative Instructor X, which is gonna give us six x y maestro of X, that would be equal to zero. And Dan mutated, rooted in respect to lie. And we get three y squared plus three x squared one is 12 who are and ask into equal to zero. Okay, So next can do, uh, we can China's solve this right here. So six x wise and we could to 12 x. As you can see, the exes can cancel out here and we get six flies through the toe. Why is equal to two? Okay, so that lives in constitute. We could use that her on the other side over here and we're going to get to square is all four Times Street, which is 12 artistry X square minus two times 12 which is last 24. So three x squared that some people deserve It's gonna be equal to positive 12 when you bring the 12. And in April 20 forward to the other side. X squared isn't me equal to four. No, X is gonna be equal to positive and negative too. So that means now that we have to possible points of Oshima So we have to to and negative too, too far to Paul supporters If you want to work, if you want to work out to figure out what those points are, so we'll have on why I want to The third power this a plus three excludes. There's gonna be times life. So it's gonna be three times four times two minus six times four minus six times for plus two and is a poor too to positive from so that we're gonna get a place for testers. 12 times two is 24. They're going to get it. Mine is 24 0 yeah? And then we're gonna get that again because to so CD sweep in and cancel out we're going to get 10 minus 24 gonna get negative 14 and it for a negative to to we're gonna get the exact same the exact same value. We're gonna get negative 14 again. Okay, so now they're trying to figure out if these are maximums on minimum, or maybe possibly saddle point. So to do that when we define effort X X, that is gonna be six. Why minus 12 effort? Why? Why is then going to be equal to six? Why? Minus 12 again and then X Y is gonna be six X. Okay, so now let's try and find With D is he's gonna be be for two. It's gonna be equal to f of x x. So that's gonna be told my soul zero sometimes effort Why? Which is again zero minus f of X y squared, which is gonna be six times X She's 12 square, so 1 44 and that is less than zero. So to two is a saddle point. And then let's do the same for deal mega to to that's going to give us again. Zero time. Zero minus 1 44 Less than zero. Suddenly Snegur to to also saddle point


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