suppose $f'$ is continuous on [a,b] and $\epsilon>0$. Prove that:
$\exists \delta>0$ s.t. $|(f(t)-f(x)/(t-x)) - f'(x)|<\epsilon$
whenever $0<|t-x|<\delta$
with $a\leq x \leq b$, $a\leq t \leq b$.
I'm having a lot of problems with this problem. It is #8 from chapter 5 in baby Rudin. Can anyone offer some helpful insights here? Thanks!