Find the unit vector?

Question

Let f(x, y, z)=yz+xz-6. At the point x=1, y=1, z=1, find the unit vector that points in the direction for which f is increasing at the fastest rate.

Answer 1

f(x,y,z) will change the fastest in the direction of the gradient vector. Evaluating the f's gradient vector at the point (1,1,1) will give you your desired vector. To change it into a unit vector simply divide each component by the magnitude of the vector