Question

maximum of directional derivative​

Answer 1

Given a function f of two or three variables and point x (in two or three dimensions), the maximum value of the directional derivative at that point, Duf(x), is |Vf(x)| and it occurs when u has the same direction as the gradient vector Vf(x).

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Answer 2

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==> The maximum value of the directional derivative occurs when ∇f and the unit vector point in the same direction. Therefore, we start by calculating ∇f(x,y): fx(x,y)=6x−4yandfy(x,y)=−4x+4y,so∇f(x,y)=fx(x,y)i+fy(x,y)j=(6x−4y)i+(−4x+4y)j.

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