Suppose $f \left( x, y, z \right) = \frac{x}{y} + \frac{y}{z}$, $P = \left( 4, 3, 3 \right)$.

A. Find the gradient of f.
$\nabla f =$ $\mathbf{i} +$ $\mathbf{j} +$ $\mathbf{k}$
Note: Your answers should be expressions of x, y and z; e.g. "3x - 4y"

B. What is the maximum rate of change of f at the point P?