Showing that $\frac{f(x)-f(x-h)}{h} \le f'(x) \le \frac{f(x+h)-f(x)}{h}$ given that f' is increasing We are considering that $h > 0$. I just don't really know how to approach this question; it seems that by taking the limit of the inequality as h goes to 0, each part of the inequality is going to be equal to $f'$, but I don't really understand why the fact that $f'$ is increasing is relevant to finding a solution to this question (and how to answer the question based on that constraint).

HINT
Use The mean value theorem on $[x-h, x]$ and $[x, x+h]$ intervals
