Find the Direction $\theta$ In Which the Directional Derivative of the Function

Find the direction $\theta$ in which the directional derivative of the function $f ( x , y ) = x y + y ^ { 2 }$ at the point $( 1,1 )$ is maximum.

A) $\cot ^ { - 1 } 2$

B)
$\cot ^ { - 1 } 3$
C) $\cos ^ { - 1 } \frac { 1 } { 2 }$
D) $\cos ^ { - 1 } \frac { 1 } { 3 }$
E) $\sin ^ { - 1 } \frac { 1 } { 2 }$
F)
$\sin ^ { - 1 } \frac { 1 } { 3 }$

G)
$\tan ^ { - 1 } 2$

H) $\tan ^ { - 1 } 3$

Correct Answer:

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