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maximum value of the directional derivative

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Let f(x,y) = x^2 - y^3

a) Find the gradient of f(x,y) at (3,2).

b) compute the directional derivative (triangle u) f(3,2) where u is the unit vector in the direction of v = <4,3>

c) Find the maximum value of the directional derivative of f(x,y) at (3,2) and the direction in which it occurs.

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The two dimensional gradient operator is expressed clearly.

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