Mean Value Theorem

An extension of Rolle’s Theorem, it says the following:

Definition

If $f$ is continuous over a closed interval $[a,b]$, and differentiable over the open interval $(a,b)$, then there exists a point $c\in (a,b)$ (Intermediate Value Theorem). The tangent to the function $f$ at this point $c$ is parallel to the secant line connecting $(a,f(a))$ and $(b,f(b))$.

Simply: The slope from the beginning to end point is the same as at least one other tangent line to the graph.