Find the maximum and minimum values of the function f(x, y, z, u, v) = x² + y² + z² + u² + v² subject to the constraints x + y + 3z = 7 and 3z - u -v = 13. A) maximum 19, occurs at the point (x, y, z, u, v) = (- 1, -1, 3, -2, -2) and no minimum value B) minimum 19, occurs at the point (x, y, z, u, v) = (- 1,- 1, 3, -2, -2) and no maximum value C) maximum 89, occurs at the point (x, y, z, u, v) = (1, 1, -9, 2, 2) and no minimum value D) minimum 0, occurs at the point (x, y, z, u, v) = (0, 0, 0, 0, 0) and no maximum value E) There are no finite extreme values.

Question

Quizplus · Accepted Answer

The minimum value of the function subject to the given constraints is 19, occurring at the point (-1, -1, 3, -2, -2). The function is a sum of squares, which is always non-negative, and the constraints define a plane, so there is no maximum value.

Find the Maximum and Minimum Values of the Function F(x