Find All the Local Maxima, Local Minima, and Saddle Points $$f ( x , y ) = x ^ { 3 } + y ^ { 3 } - 243 x - 48 y - 5$$

question 406

Multiple Choice

Find all the local maxima, local minima, and saddle points of the function.
- $$f ( x , y ) = x ^ { 3 } + y ^ { 3 } - 243 x - 48 y - 5$$

• A) f(9, -4) = -1335, saddle point; f(-9, 4) = 1325, saddle point
• B) f(-9, -4) = 1581, local maximum; f(9, 4) = -1591, local minimum
• C) f(-9, -4) = 1581, local maximum
• D) f(9, 4) = -1591, local minimum; f(9, -4) = -1335, saddle point; f(-9, 4) = 1325, saddle point; f(-9, -4) = 1581, local maximum

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