Question

Explain Mean Value Theorem

Answer 1

For any function $f\left(x\right)$

1. $f\left(x\right)$ is defined and continuous on the interval $[a,b]$
2. $f\left(x\right)$ is differentiable on $(a,b)$

Then there exists one number $c$ such that

$f^{\prime }\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$, where $a<c<b$