Mean Value Theorem of Differential Calculus

analysis

Definition

Mean Value Theorem of Differential Calculus

Let $f$ be a continuous function on the closed interval $[a,b]$ and differentiable on the open interval $(a,b)$. Then there exists a point $\xi \in (a,b)$ such that:

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