Question

Find the relative maximum and minimum values of f(x, y) = x² + xy + y² - 28y + 261.

Answer 1

To find the relative maximum and minimum values of the function f(x, y) = x² + xy + y² - 28y + 261, we need to take the partial derivatives with respect to x and y and set them equal to zero. Then, we can use the second derivative test to determine if the critical points are relative maximum or minimum values.

Step-by-step explanation:

To find the relative maximum and minimum values of the function f(x, y) = x² + xy + y² - 28y + 261, we need to take the partial derivatives with respect to x and y and set them equal to zero.

First, we find the partial derivative with respect to x:

∂f/∂x = 2x + y

Then, we find the partial derivative with respect to y:

∂f/∂y = x + 2y - 28

Setting these two equations equal to zero and solving for x and y will give us the critical points. Then, we can use the second derivative test to determine if these critical points are relative maximum or minimum values.