Let $f ( x , y ) = x ^ { 2 } y + y ^ { 2 }$ and $\mathbf { u } = \frac { 1 } { 2 } \mathbf { i } + \frac { \sqrt { 3 } } { 2 } \mathbf { j }$ Then the directional derivative of f at (-1, 2) in the direction of $\mathbf { U }$ is

A) $\frac { - 2 + 5 \sqrt { 3 } } { 2 }$
B) $\frac { 4 - 5 \sqrt { 3 } } { 2 }$
C) $\frac { - 4 + 5 \sqrt { 3 } } { 2 }$
D) $\frac { - 4 - 5 \sqrt { 3 } } { 2 }$
E) $\frac { 4 + 5 \sqrt { 3 } } { 2 }$

Question

Let

f ( x , y ) = x ^ { 2 } y + y ^ { 2 }

and

\mathbf { u } = \frac { 1 } { 2 } \mathbf { i } + \frac { \sqrt { 3 } } { 2 } \mathbf { j }

Then the directional derivative of f at (-1, 2) in the direction of

\mathbf { U }

is

A) $\frac { - 2 + 5 \sqrt { 3 } } { 2 }$
B) $\frac { 4 - 5 \sqrt { 3 } } { 2 }$
C) $\frac { - 4 + 5 \sqrt { 3 } } { 2 }$
D) $\frac { - 4 - 5 \sqrt { 3 } } { 2 }$
E) $\frac { 4 + 5 \sqrt { 3 } } { 2 }$

Quizplus · Accepted Answer

The Answer is C

Let f(x,y)=x2y+y2f ( x , y ) = x ^ { 2 } y + y ^ { 2 }f(x,y)=x2y+y2

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