Find all the local maxima, local minima, and saddle points of the function.
-$$f ( x , y ) = \left( x ^ { 2 } - 9 \right) ^ { 2 } + \left( y ^ { 2 } - 16 \right) ^ { 2 }$$
A) f(0, 0) = 337, local maximum; f(-3, -4) = 0, local minimum
B) f(0, 0) = 337, local maximum; f(0, 4) = 81, saddle point; f(3, 0) = 256, saddle point; f(3, 4) = 0, local minimum; f(-3, -4) = 0, local minimum
C) f(0, 0) = 337, local maximum; f(0, 4) = 81, saddle point; f(0, -4) = 81, saddle point; f(3, 0) = 337, saddle point; f(3, 4) = 0, local minimum; f(3, -4) = 0, local minimum;
F(-3, 0) = 256, saddle point; f(-3, 4) = 0, local minimum; f(-3, -4) = 0, local minimum
D) f(0, 0) = 337, local maximum; f(3, 4) = 0, local minimum; f(3, -4) = 0, local minimum; f(-3, 4) = 0, local minimum; f(-3, -4) = 0, local minimum

Question

Quizplus · Accepted Answer

The Answer of Find all the local maxima, local minima, and saddle points of the function.
-$$f ( x , y ) = \left( x ^ { 2 } - 9 \right) ^ { 2 } + \left( y ^ { 2 } - 16 \right) ^ { 2 }$$
A) f(0, 0) = 337, local maximum; f(-3, -4) = 0, local minimum
B) f(0, 0) = 337, local maximum; f(0, 4) = 81, saddle point; f(3, 0) = 256, saddle point; f(3, 4) = 0, local minimum; f(-3, -4) = 0, local minimum
C) f(0, 0) = 337, local maximum; f(0, 4) = 81, saddle point; f(0, -4) = 81, saddle point; f(3, 0) = 337, saddle point; f(3, 4) = 0, local minimum; f(3, -4) = 0, local minimum;
F(-3, 0) = 256, saddle point; f(-3, 4) = 0, local minimum; f(-3, -4) = 0, local minimum
D) f(0, 0) = 337, local maximum; f(3, 4) = 0, local minimum; f(3, -4) = 0, local minimum; f(-3, 4) = 0, local minimum; f(-3, -4) = 0, local minimum

Find All the Local Maxima, Local Minima, and Saddle Points f(x,y)=(x2−9)2+(y2−16)2f ( x , y ) = \left( x ^ { 2 } - 9 \right) ^ { 2 } + \left( y ^ { 2 } - 16 \right) ^ { 2 }f(x,y)=(x2−9)2+(y2−16)2

Find All the Local Maxima, Local Minima, and Saddle Points $f ( x , y ) = \left( x ^ { 2 } - 9 \right) ^ { 2 } + \left( y ^ { 2 } - 16 \right) ^ { 2 }$