Mean Value Theorem of Differentiation

Let $y=f(x)$ be a continous function on closed interval [a,b] and differentiatable on the open interval (a,b). There exists a c, a<c<b where:

$$\begin{array}{r}{f}^{\prime }(c)=\frac{f(b)-f(a)}{b-a}\end{array}$$

That is, there’s a value c in (a,b) where the intantateous rate of change of f and c is equal to the average change on f between [a,b].