The figure below shows the level curves of the function f(x, y). Estimate the di

Question

The figure below shows the level curves of the function f(x, y). Estimate the directional derivative: D u f(3, 3) where u = (-i -j)/root 2 Hint: Starting at the point P you are given, move along the line with direction vector u until you hit a nearby contour going through a grid point Q = P + hu whose coordinates you can determine. Consider the line on both sides of the given point (directions + u). Then estimate the directional derivative as Vertical change / horizontal change = (f(Q) - f(P))/h.

Explanation / Answer

P=(3,3),in the direction of u==>Q=(1,1)

Duf(3,3)=(5-5)/[(3-1)2 +(3-1)2]

Duf(3,3)=(0)/[4+4]

Duf(3,3)=0

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