Continuity/Differentiability Question

Suppose is differentiable on [a,b] (with one sided derivatives at the end points). Show that if then the minimum of f is attained at a point . Note: You may not assume the derivative of f is continuous.

My first thoughts was just to use IVT on the derivative until I saw the note, now I'm not sure what to do. Any help where to start?

Re: Continuity/Differentiability Question

And just so you know, the IVT property also holds for derivatives, regardless of differentiability.