Consider the following function​ f, point​ P, and unit vector Bold u . 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/√3,1/√3,−1/√3⟩