Explanation Given : f ( x ) = | 2 − 3 x | , K = 2 Concept used: Intermediate value theorem: Intermediate value theorem states that if f is a continuous function whoch domain contains the interval [ a , b ] , then it takes on any given value between f ( a ) and f ( b ) at some point within the interval f ( c ) = K where c ∈ ( a , b ) . Continuity: The function f is continuous at x = c if f ( c ) is defined and if lim → x → c f ( x ) = f ( c ) . Calculation: f ( x ) = | 2 − 3 x | , K = 2 be a given function. It has to find interval [ a , b ] , and value K there is some c ∈ ( a , b ) for which f ( c ) = K

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Chapter 1.4, Problem 66S

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To show:A fuction f has a value K , there must be some c∈ℝ for which f(c)=K by using the intermediate value theorem and find or approximateonesuch value of c .

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Chapter 1.4, Problem 65S

Chapter 1.4, Problem 67S

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Chapter 1 Solutions

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A fuction f has a value K , there must be some c ∈ ℝ for which f ( c ) = K by using the intermediate value theorem and find or approximateonesuch value of c .

Solution Summary: The author states that if f is a continuous function, it takes on any given value at some point within the interval.

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To show:A fuction f has a value K , there must be some c∈ℝ for which f(c)=K by using the intermediate value theorem and find or approximateonesuch value of c .

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Chapter 1 Solutions