Q:

A question in proof of Fermat's Theorem on stationary points

In the proof of Fermat's Theorem on stationary points, why is it true that if $h>0$ then $\frac{f(x_0+h)-f(x_0)}{h}\leq 0$? Why can we conclude that from $h>0?$
Note: the proof can be found at this link http://planetmath.org/proofoffermatstheoremstationarypoints

A:

If $x_0$ is a local maximum for $f$, then $f(x_0+h)\leq f(x_0)$ for all sufficiently small $h$. 
Therefore $f(x_0+h)-f(x_0)\leq 0$, so if $h>0$ then $\frac{f(x_0+h)-f(x_0)}{h}\leq 0$.

