Find all the local maxima, local minima, and saddle points of the function.
-$$f ( x , y ) = \left( x ^ { 2 } - 81 \right) ^ { 2 } - \left( y ^ { 2 } - 64 \right) ^ { 2 }$$
A) f(0, 0) = 2465, saddle point; f(0, 8) = 6561, local maximum; f(0, -8) = 6561, local maximum; f(9, 0) = -4096, local minimum; f(9, 8) = 0, saddle point; f(9, -8) = 0, saddle point;
F(-9, 0) = -4096, local minimum; f(-9, 8) = 0, saddle point; f(-9, -8) = 0, saddle point
B) f(0, 0) = 2465, saddle point; f(9, 8) = 0, saddle point; f(9, -8) = 0, saddle point; f(-9, 8) = 0, saddle point; f(-9, -8) = 0, saddle point
C) f(0, 0) = 2465, saddle point; f(0, 8) = 6561, local maximum; f(9, 0) = -4096, local minimum
D) f(0, 8) = 6561, local maximum; f(0, -8) = 6561, local maximum; f(9, 0) = -4096, local minimum; f(-9, 0) = -4096, local minimum

Question

Quizplus · Accepted Answer

The function has saddle points at (0, 0), (9, 8), (9, -8), (-9, 8), and (-9, -8). It has local maxima at (0, 8) and (0, -8), and local minima at (9, 0) and (-9, 0).

Find All the Local Maxima, Local Minima, and Saddle Points f(x,y)=(x2−81)2−(y2−64)2f ( x , y ) = \left( x ^ { 2 } - 81 \right) ^ { 2 } - \left( y ^ { 2 } - 64 \right) ^ { 2 }f(x,y)=(x2−81)2−(y2−64)2

Find All the Local Maxima, Local Minima, and Saddle Points $f ( x , y ) = \left( x ^ { 2 } - 81 \right) ^ { 2 } - \left( y ^ { 2 } - 64 \right) ^ { 2 }$