Question

Find the absolute maximum and minimum values of f on the set d. f(x, y) = 7xy - x - 2y, where d is the closed triangular region with vertices (1, 0), (5, 0), and (1, 4).

Answer 1

To find the absolute maximum and minimum values of the function f(x, y) = 7xy - x - 2y on the set d, evaluate the function at its critical points and endpoints.

Step-by-step explanation:

To find the absolute maximum and minimum values of the function f(x, y) = 7xy - x - 2y on the set d, we need to evaluate the function at its critical points and endpoints.

First, we find the critical points by taking the partial derivatives of f with respect to x and y and setting them equal to zero:

• ∂f/∂x = 7y - 1 = 0 => y = 1/7
• ∂f/∂y = 7x - 2 = 0 => x = 2/7

Next, we evaluate f at the critical points and at the vertices of the triangular region to determine the absolute maximum and minimum values.