Lagrange Mean Value Theorem

Lagrange Mean Value Theorem

If $$f(x)$$ is continuous on $$[a,b]$$ and differentiable on $$(a,b)$$, then there exists at least one $$c\in(a,b)$$ such that:

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

Usage

- Used to relate the instantaneous rate of change at some point to the average rate of change over an interval.