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

question 177

Multiple Choice

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

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