How can i prove that;

if f is a differentiable function on [a,b] where f '(a) < 0 and f '(b)>0, there exists a point c in the set of (a,b) at which f '(c) = 0, and i can't assume the function is continuous.

This makes perfect sense to me intuitively yet i'm having trouble proving it am not sure which theorem helps here if any and where exactly to start.

Cheers,