The extreme values of the function f(x , y, z) = 23 x + y²z subject to the constraintsx - z = 0 and y² + z² = 36 are given by: A) 115, 128 B) - 115, 115 C) -128, 115 D) -128, 128 E) -128, -115

Question

Quizplus · Accepted Answer

The constraints x = z and y² + z² = 36 imply that z² = 36 - y². Substituting x = z into the function gives f(z, y, z) = 23z + y²z. Solving for extreme values using these constraints, we find the maximum and minimum values of the function are 128 and -128.

The Extreme Values of the Function F(x , Y, Z)