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.
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