Mean Value Theorem

The Average Value Theorem states that if $f(x)$ is continuous on an interval $[a,b]$ , then there exists a $c$ in $[a,b]$ such that

$f(c)=\dfrac{1}{b-a}\int_{a}^{b}f(x)dx$

In words, there is a number $c$ in $[a,b]$ such that $f(c)$ equals the average value of the function in the interval $[a,b]$ .

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