Mean value theorem

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The Mean value theorem of Calculus states that for some value c on the function f on some interval [a, b], f'(c) (the slope of f at c) will equal the average slope over [a, b], provided that f is continuous over the interval [a, b] and differentiable on the interval (a, b).

This is written algebraically as: f(b) − f(a) = f'(c)(ba), where c is between b and a.

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