Find All the Local Maxima, Local Minima, and Saddle Points $$f ( x , y ) = 6 x ^ { 2 } y + 5 x y ^ { 2 }$$

Multiple Choice

Find all the local maxima, local minima, and saddle points of the function.
- $$f ( x , y ) = 6 x ^ { 2 } y + 5 x y ^ { 2 }$$

A) $f ( 30,30 ) = 297,000$ , local maximum
B) $\left\{ \left( \frac { 1 } { 5 } , \frac { 1 } { 6 } \right) = \frac { 61 } { 900 } \right.$ , local minimum
C) $\mathrm { f } ( 0,0 ) = 0$ , saddle point
D) $\left\{ \left( \frac { 1 } { 6 } , \frac { 1 } { 5 } \right) = \frac { 1 } { 15 } \right.$ , local minimum