Mean Value Theorem

• categories: Real Analysis, Theorem

The Mean Value Theorem (MVT) states that if a function $f$ is continuous on the closed interval $[a,b]$ and differentiable on the open interval $(a,b)$, then there exists at least one point $c\in (a,b)$ such that:

$f^{\prime }(c)=\frac{f(b)-f(a)}{b-a}$

This means that the instantaneous rate of change (the derivative) at some point $c$ is equal to the average rate of change over the interval $[a,b]$.