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) $\tan ^ { - 1 } 3$

Question

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) $\tan ^ { - 1 } 3$

Quizplus · Accepted Answer

The directional derivative is maximum in the direction of the gradient. The gradient of $f(x, y) = xy + y^2$ at $(1, 1)$ is $(1, 3)$. The direction $\theta$ is given by $\tan^{-1} \frac{3}{1} = \tan^{-1} 3$.

Find the Direction θ\thetaθ In Which the Directional Derivative of the Function

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