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

Question 200

Essay

If f(x,y)=2x2+4y2−xyf ( x , y ) = 2 x ^ { 2 } + 4 y ^ { 2 } - x y , find the gradient at the point (2,1)( 2,1 ) . Also find the rate of change of f(x,y)f ( x , y ) in the direction θ=π3\theta = \frac { \pi } { 3 } at (2,1)( 2,1 ) .

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