Suppose $fâ(a) = M$ where $M > 0$. Prove that there is a $\delta>0$ such that if $0<|x-a|<\delta$, then $\frac{f(x)-f(a)}{x-a} > M/2$.
I am probably making this problem harder than it is. I would appreciate a push in the right direction. The solution isn't coming to me. Thanks!