Use the contour diagram for f(x, y) shown below to estimate the directional deri

Question

Use the contour diagram for f(x, y) shown below to estimate the directional derivative of f in the direction v vector at the point P. (a) At the point P = (2, 2) in the direction v vector = i vector, the directional derivative is approximately _____ (b) At the point P = (3, 2) in the direction v vector = -i vector, the directional derivative is approximately ______ (c) At the point P = (1, 4) in the direction v vector = (i vector + j vector)/squareroot 2, the directional derivative is approximately _____ (d) At the point P = (1, 0) in the direction v vector = -i vector, the directional derivative is approximately ____

Explanation / Answer

Direction is v = i +0j

Hence directional derivative =1*4 +0*4 = 4

B) similarly directional derivative = -1*6+0*6 = -6

C) 4/sqrt(2) +2/ sqrt(2) = 4sqrt(2)

D)0

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