Dear all, suppose $\displaystyle f$ is a continous function on [TEX[a,b][/TEX]. $\displaystyle E\subset[a,b]$ is countable. Assume $\displaystyle f$ is differentiable on $\displaystyle [a,b]\backslash E$, the the derivative $\displaystyle >=0$. Show that $\displaystyle f(a)\leq f(b).$

Note: We assume only that $\displaystyle f$ is differentiable on $\displaystyle [a,b]\backslash E.$

I do not know how to prove. Do you know? Help me, thank you...