Let f be differentiable on (a, b) and continuous on [a, b]. Then there is at least one point c in (a, b) where 
 

Proof:
 

 We will appeal to the picture below instead of completing a formal proof.

What is the above tangent slope in calculus notation?

What is the formula for the above secant slope?

What is the relationship between these two slopes?    (See answer below.)