How do I PROOF the following?

3. Let f (3:) be a continuous function on the interval [09, b] and differen tiable on the interval (a, b). If u.) = 10 and the derivative of f(:L') is 0 on the interval (a,b), i.e. f'(x) = 0 on ((1,1)), then f(x) = 10 on the interval [0, b]