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

question 176

Multiple Choice

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

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