Suppose f: [0,2]-> R is differentiable. f(0)=0, f(1)=2 and f(2)=2. Prove that

1. There is $\displaystyle c_1$ such that f'($\displaystyle c_1$) =0

2. There is $\displaystyle c_2$ such that f'(c_2)=2 and

3. There is $\displaystyle c_3$ such that f'($\displaystyle c_3$=1/2