Find the Largest Value of the Directional Derivative of the Function

Multiple Choice

Find the largest value of the directional derivative of the function $f ( x , y ) = \frac { y } { x + y }$ at the point $( x , y ) = ( 1,2 )$ .

A) $\sqrt { 5 }$

B) $\frac { 5 } { 9 }$
C) $- \sqrt { 5 }$
D) $- \frac { 5 } { 9 }$
E) $\frac { \sqrt { 5 } } { 3 }$
F) $\frac { \sqrt { 5 } } { 9 }$

G) $- \frac { \sqrt { 5 } } { 3 }$

H) $- \frac { \sqrt { 5 } } { 9 }$