Let f be a function that is differentiable on the open interval (1,10). If f(2)=-5, f(5)=5, and f(9)=-5, which of the following must be true?

I. f has at least 2 zeros
II. The graph of f has at least one horizontal tangent
III. For some c, c is greater then 2 but less then 5, f(c)=3

Question

Let f be a function that is differentiable on the open interval (1,10). If f(2)=-5, f(5)=5, and f(9)=-5, which of the following must be true?
 
I. f has at least 2 zeros
 II. The graph of f has at least one horizontal tangent
 III. For some c, c is greater then 2 but less then 5, f(c)=3

abb0t · Answer

This is referring to Mean Value Theorem, I believe. Yes?