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).

15 batches are the most you can make

step-by-step explanation:

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11