http://www.mathcs.org/analysis/reals/cont/proofs/rollethm.html"Assume for now that f(c) # 0 is a maximum. Since f(a) = f(b) = c we know that c is in (a, b), and therefore f is differentiable at c. Note that f(x) f(c) since f(c) is a maximum. "

I think f(a)=f(b)=c is a typo, it should be f(a)=f(b)=0.

But why c is in(a,b) then we can get that f is differentiable at c? please explain.