If $f ( x , y ) = 2 x ^ { 2 } + 4 y ^ { 2 } - x y$ , find the gradient at the point $( 2,1 )$ . Also find the rate of change of $f ( x , y )$ in the direction $\theta = \frac { \pi } { 3 }$ at $( 2,1 )$ .

Question

Quizplus · Accepted Answer

The Answer of If $f ( x , y ) = 2 x ^ { 2 } + 4 y ^ { 2 } - x y$ , find the gradient at the point $( 2,1 )$ . Also find the rate of change of $f ( x , y )$ in the direction $\theta = \frac { \pi } { 3 }$ at $( 2,1 )$ .

If f(x,y)=2x2+4y2−xyf ( x , y ) = 2 x ^ { 2 } + 4 y ^ { 2 } - x yf(x,y)=2x2+4y2−xy

If $f ( x , y ) = 2 x ^ { 2 } + 4 y ^ { 2 } - x y$