Consider the following function f, point P, and vector 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)= xy+yz+xz+3; P(1,-1,8); (0, -1/sqrt(2), 1/sqrt(2))