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Lesson: The Intermediate Value Theorem

In this lesson, we will learn one of the most intuitive theorems: the intermediate value theorem. The theorem states that if L is a value between f(b) and f(a), there must be a value c where f(c) = L.

Worksheet: The Intermediate Value Theorem • 2 Questions

Q1:

The function satisfies and . But there is no between and 1 where . Why does this not violate the intermediate value theorem?

Abecause the function is not defined on the entire interval
Bbecause the intermediate value theorem only applies on the interval
Cbecause the intermediate value theorem only applies to polynomial functions
Dbecause the intermediate value theorem only applies to cases where , not
Ebecause the function is not continuous over its domain

Q2:

The figure shows the graph of the function on the interval together with the dashed line .

and , but anywhere on . Why does this not violate the intermediate value theorem?

Abecause the function is not continuous at
Bbecause the intermediate value theorem only applies to functions with at some value
Cbecause the function is not defined on the entire interval
Dbecause the intermediate value theorem only applies to polynomial functions
Ebecause the intermediate value theorem only applies to cases where not where

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