explain why the following statements are true or false

Question

a) if f is continuous on [2,5] and differentiable on (2,5) and f(2)=0 and f(5)=0, then there is a real number c between 2 and 5 where f’(c)=0.

b) if f is continuous on [2,5] then there is an absolute maximum and an absolute minimum on [2,5].

c) If f is continuous on [2,5] and differentiable on (2,5) and f(2)=6 and f(5)=15, then there is a number c between 2 and 5 where f’(c)=3.

Answer 1

a) Rolle's theorem

b) Intermediate Value Theorem

c) Mean Value Theorem