Question: Consider the following functions f, points P, and unit vectors u. a. Compute the gradient of f and evaluate it at P. b. Find the

Consider the following functions f, points P, and unit vectors u.f(x, y, z) = 1 + 4xyz; P(1,-1,1); 1 1 /3' 3


a. Compute the gradient of f and evaluate it at P.


b. Find the unit vector in the direction of maximum increase of f at P.


c. Find the rate of change of the function in the direction of maximum increase at P.


d. Find the directional derivative at P in the direction of the given vector.

f(x, y, z) = 1 + 4xyz; P(1,-1,1); 1 1 /3' 3 3

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