Consider the following function f, point P, and unit 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.
$f(x,y,z) = xy + yz + xz + 8; P(7, -7,8); \left(0, \frac{1}{\sqrt{2}}, -\frac{1}{\sqrt{2}}\right)$
a. $\nabla f(x,y,z) = \langle y+z, z+x, x+y \rangle$
$\nabla f(7, -7,8) = $