CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 14. Concepts of Calculus

14.7 Intermediate and Extreme Value Theorems

Here you will use continuity to explore the intermediate and extreme value theorems.
While the idea of continuity may seem somewhat basic, when a function is continuous over a closed interval like
x∈[ 1 , 4 ], you can actually draw some major conclusions. The conclusions may be obvious when you understand
the statements and look at a graph, but they are powerful nonetheless.
What can you conclude using the Intermediate Value Theorem and the Extreme Value Theorem about a function that
is continuous over the closed intervalx∈[ 1 , 4 ]?

Watch This

MEDIA

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URL: http://www.ck12.org/flx/render/embeddedobject/62353

http://www.youtube.com/watch?v=6AFT1wnId9U Intermediate Value Theorem

Guidance

TheIntermediate Value Theoremstates that if a function is continuous on a closed interval anduis a value between
f(a)andf(b)then there exists ac∈[a,b]such thatf(c) =u.