This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x, y) = x2 − y2; x2 + y2 = 64

Maximum at points (8,0),(-8,0).Minimum at points (0,8), (0,-8).

Step-by-step explanation:

There are multiple ways of using lagrange multipliers. Most of them are equivalent.

Consider the function . We want the following .

Then, we have

From the first two equations, we can see that if then necessarily y=0. IN that case, from the third equation (which is the restriction) gives us that .

On the other hand, if then necessarily x=0. Again, using the restriction this gives us that .

if we evaluate the original function in this points, we have that . Then, we have Maximum at points (8,0),(-8,0) and Minimum at points (0,8), (0,-8).

answer: what are the following choices

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