Let $f ( x , y ) = \frac { x y } { x ^ { 2 } + y ^ { 2 } }$ . Then the maximum value of the directional derivative $D _ { \mathrm { u } } f ( - 1,2 )$ is

A)3
B) $\frac { 3 \sqrt { 5 } } { 25 }$
C) $\frac { 3 } { 5 }$
D) $\frac { 1 } { 3 }$
E)5

Question

Let $f ( x , y ) = \frac { x y } { x ^ { 2 } + y ^ { 2 } }$ . Then the maximum value of the directional derivative $D _ { \mathrm { u } } f ( - 1,2 )$ is

A)3
B) $\frac { 3 \sqrt { 5 } } { 25 }$
C) $\frac { 3 } { 5 }$
D) $\frac { 1 } { 3 }$
E)5

Quizplus · Accepted Answer

The maximum value of the directional derivative is $\frac { 3 \sqrt { 5 } } { 25 }$ and it occurs in the direction of the vector $( 2 , 1 )$.

Let f(x,y)=xyx2+y2f ( x , y ) = \frac { x y } { x ^ { 2 } + y ^ { 2 } }f(x,y)=x2+y2xy​

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