MATH114 Chapter Notes - Chapter 2.5: Intermediate Value Theorem, Maxima And Minima

• School: University of Alberta
• Department: Mathematics
• Course: MATH114
• Professor: Vincent Bouchard

Document Summary

Intermediate value theorem (ivt): let f be a function that is continuous over [a, b], and let n be any number between f (a) and f (b). Then there exists a number c (a, b) such that f (c) = n . Bisection method: to locate the roots of a function f using the ivt: find two points a and b such that f (a) < 0 and f (b) > 0. Then, by ivt there must be a root of f between a and b: consider the midpoint c = (a + b)/2. Then: if f (c) < 0, by ivt there must be a root of f between c and b. Mean value theorem (mvt): let f be a function that is continuous over [a, b] and di erentiable over (a, b). Then there is a number c (a, b) such that f(cid:48)(c) = f (b) f (a)