Chapter 13, Problem 8RE

Let $z=f\left(x,y\right).$

(a) Express $\partial z/\partial x$ and $\partial z/\partial y$ as limits.

(b) In words, what do the derivatives $f_x(x_0,y_0)\text{and}{f}_y(x_0,y_0)$ tell you about the surface $z=f(x,y)$

(c) In words, what do the derivatives $\partial z/\partial x(x_0,y_0)$ and $\partial z/\partial y(x_0,y_0)$ tell you about the rates of change of z with respect to x and y?