Find the Second Directional Derivative Of $f ( x , y ) = x ^ { 2 } e ^ { y }$

Multiple Choice

Find the second directional derivative of $f ( x , y ) = x ^ { 2 } e ^ { y }$ at the point $( 2,0 )$ in the direction $(3 , - 4 )$ .

A) $\frac { 14 } { 5 }$

B) $\frac { 4 } { 5 }$
C) $\frac { 14 } { 25 }$
D) 14
E) $- \frac { 14 } { 5 }$
F) $- \frac { 4 } { 5 }$

G) $- \frac { 14 } { 25 }$
H) $- 14$