Cauchy's Mean Value Theorem

Cauchy's Mean Value Theorem

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

$$\left[f(b)-f(a)\right]g'(c)=\left[g(b)-g(a)\right]f'(c)$$

Usage

- Used when two functions are involved and the ordinary Mean Value Theorem is not directly applicable.