Question

This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliens to find the extreme values of the function cubject to the given constraint. R(x,y)=9xe y ,x 2 +y 2 −2

Maximum value = ______
Minimum value= ________

Answer 1

To find the extreme values of the function R(x, y) = 9xe^y, subject to the constraint x^2 + y^2 - 2 = 0, we can use Lagrange multipliers.

Step-by-step explanation:

To find the extreme values of the function R(x, y) = 9xe^y, subject to the constraint x^2 + y^2 - 2 = 0, we can use Lagrange multipliers.

Step 1: Set up the Lagrangian function L = R(x, y) - λ(g(x, y)), where g(x, y) is the constraint function.

Step 2: Calculate the partial derivatives of L with respect to x, y, and λ, and set them equal to zero.

Step 3: Solve the resulting equations to find the critical points.

Step 4: Evaluate R(x, y) at the critical points to find the maximum and minimum values.

In this case, the maximum value is ______ and the minimum value is ______.