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Mean Value Theorem

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The Mean Value Theorem states that if a < b are real numbers and the function f:[a,b] \to \mathbb{R} is continuous on the interval [a,b], then there exists a value 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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