bolzano theorem
Assuming "bolzano theorem" is a calculus result | Use as instead

Input interpretation

Bolzano theorem (calculus result)

Theorem

Let f(x) be a real-valued function that is continuous on the closed interval [a, b]. If there are two values x_1 and x_2 with x_1<x_2 in the interval [a, b] for which f(x_1) f(x_2)<0 (that is, f(x_1) and f(x_2) have different signs), then there is at least one value x_0 in the open interval (x_1, x_2) for which f(x_0) = 0.

Details

Concepts involved

closed interval | continuous function

Extension

intermediate value theorem

Related concept

mean value theorem

Associated people

Jean-Gaston Darboux | Augustin-Louis Cauchy | Joseph-Louis Lagrange | Bernard Placidus Johann Nepomuk Bolzano | Bryson of Heraclea
POWERED BY THE WOLFRAM LANGUAGE

Related Queries:

Have a question about using Wolfram|Alpha?Contact Pro Premium Expert Support »

Give us your feedback »