Let f:R--->R twice differentiable on R. Suppose that f(a)=f(b)=f(c) for real numbers a<b<c. show that there exists cE(a,c) such that $\displaystyle f''(d)=0$

do I apply Mean Value Theorem to the interval (a,c)? why do i need the function to be twice differentiable to answer the question?

thanks