intermediate value theorem - Wolfram|Alpha

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Input interpretation

intermediate value theorem (calculus result)

Theorem

Let f(x) be a real-valued function that is continuous on the closed interval [a, b]. Then for every value y_0 between f(a) and f(b), there is a value x_0 in [a, b] such that f(x_0) = y_0, meaning that f(x) assumes all intermediate values between f(a) and f(b).

Details

Concepts involved

closed interval | continuous function

Specific cases

Rolle's theorem

Related concepts

mean value theorem | Bolzano theorem

Associated people

Jean-Gaston Darboux | Augustin-Louis Cauchy | Joseph-Louis Lagrange | Bryson of Heraclea

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