Find the absolute maxima and minima of the function on the given domain.
-$$f ( x , y ) = 4 x ^ { 2 } + 7 y ^ { 2 } \text { on the disk bounded by the circle } x ^ { 2 } + y ^ { 2 } = 9$$
A) Absolute maximum: 36 at (3, 0) and (-3, 0); absolute minimum: 0 at (0, 0)
B) Absolute maximum: 99 at (3, 3); absolute minimum: 0 at (0, 0)
C) Absolute maximum: 63 at (0, 3) and (0, -3); absolute minimum: 0 at (0, 0)
D) Absolute maximum: 63 at (0, 3) and (0, -3); absolute minimum: 36 at (3, 0) and (-3, 0)

Question

Quizplus · Accepted Answer

The function $f(x, y) = 4x^2 + 7y^2$ is minimized at the origin (0, 0) with a value of 0. On the boundary $x^2 + y^2 = 9$, the maximum occurs at (0, 3) and (0, -3) with a value of 63.

Find the Absolute Maxima and Minima of the Function on the Given