Given $f ( x , y ) = x ^ { 2 } y$

Multiple Choice

Given $f ( x , y ) = x ^ { 2 } y$ , $P _ { 0 } = ( 3,2 )$ , let $\mathbf { u }$ be the unit vector for which the directional derivative $D _ { \mathbf { u } } f \left( P _ { 0 } \right)$ has maximum value. This maximum value is

A) $\frac { 288 } { 5 }$
B) 1
C) 6
D) $12 \sqrt { 3 }$

E) 15