Explanation Given : f ( x ) = { x 2 − 9 , if x ≤ − 2 x 2 + x − 2 , if x > − 2 Concept used: Continuity: The function f is continuous at x = c if f ( c ) is defined and if lim → x → c f ( x ) = f ( c ) . 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. Calculation : f ( x ) = { x 2 − 9 , if x ≤ − 2 x 2 + x − 2 , if x > − 2 be a given function. And it has to find the intervals on which the functions is positive or negative. f ( x ) = { x 2 − 9 , if x ≤ − 2 x 2 + x − 2 , if x > − 2 The graph can be drawn as below

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Question

Chapter 1.4, Problem 74S

To determine

To find:The intervals on which function is positive or negative by using the intermediate value theorem and definition of continuity.

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Chapter 1.4, Problem 73S

Chapter 1.4, Problem 75A

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Chapter 1 Solutions

Calculus Combo

Ch. 1.1 - Prob. 1TB Ch. 1.1 - Prob. 2TB Ch. 1.1 - Prob. 0C Ch. 1.1 - Prob. 1C Ch. 1.1 - Prob. 2C Ch. 1.1 - Prob. 3C Ch. 1.1 - Prob. 4C Ch. 1.1 - Prob. 5C Ch. 1.1 - Prob. 6C Ch. 1.1 - Prob. 7C

Ch. 1.1 - Prob. 8C Ch. 1.1 - Prob. 9C Ch. 1.1 - Prob. 10C Ch. 1.1 - Prob. 11C Ch. 1.1 - Prob. 12C Ch. 1.1 - Prob. 13C Ch. 1.1 - Prob. 14C Ch. 1.1 - Prob. 15C Ch. 1.1 - Prob. 16C Ch. 1.1 - Prob. 17C Ch. 1.1 - Prob. 18C Ch. 1.1 - Prob. 19C Ch. 1.1 - Prob. 20C Ch. 1.1 - Prob. 21S Ch. 1.1 - Prob. 22S Ch. 1.1 - Prob. 23S Ch. 1.1 - Prob. 24S Ch. 1.1 - Prob. 25S Ch. 1.1 - Prob. 26S Ch. 1.1 - Prob. 27S Ch. 1.1 - Prob. 28S Ch. 1.1 - Prob. 29S Ch. 1.1 - Prob. 30S Ch. 1.1 - Prob. 31S Ch. 1.1 - Prob. 32S Ch. 1.1 - Prob. 33S Ch. 1.1 - Prob. 34S Ch. 1.1 - Prob. 35S Ch. 1.1 - Prob. 36S Ch. 1.1 - Prob. 37S Ch. 1.1 - Prob. 38S Ch. 1.1 - Prob. 39S Ch. 1.1 - Prob. 40S Ch. 1.1 - Prob. 41S Ch. 1.1 - Prob. 42S Ch. 1.1 - Prob. 43S Ch. 1.1 - Prob. 44S Ch. 1.1 - Prob. 45S Ch. 1.1 - Prob. 46S Ch. 1.1 - Prob. 47S Ch. 1.1 - Prob. 48S Ch. 1.1 - Prob. 49S Ch. 1.1 - Prob. 50S Ch. 1.1 - Prob. 51S Ch. 1.1 - Prob. 52S Ch. 1.1 - Prob. 53S Ch. 1.1 - Prob. 54S Ch. 1.1 - Prob. 55S Ch. 1.1 - Prob. 56S Ch. 1.1 - Prob. 57S Ch. 1.1 - 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Prob. 70S Ch. 1.4 - Prob. 71S Ch. 1.4 - Prob. 72S Ch. 1.4 - Prob. 73S Ch. 1.4 - Prob. 74S Ch. 1.4 - Prob. 75A Ch. 1.4 - Prob. 76A Ch. 1.4 - Prob. 77A Ch. 1.4 - Prob. 78A Ch. 1.4 - Prob. 79A Ch. 1.4 - Prob. 80A Ch. 1.4 - Prob. 81P Ch. 1.4 - Prob. 82P Ch. 1.4 - Prob. 83P Ch. 1.4 - Prob. 84P Ch. 1.4 - Prob. 85P Ch. 1.4 - Prob. 86P Ch. 1.4 - Prob. 87P Ch. 1.4 - Prob. 88P Ch. 1.4 - Prob. 89P Ch. 1.4 - Prob. 90P Ch. 1.4 - Prob. 91P Ch. 1.4 - Prob. 92P Ch. 1.4 - Prob. 93P Ch. 1.4 - Prob. 1TF Ch. 1.4 - Prob. 2TF Ch. 1.4 - Prob. 3TF Ch. 1.4 - Prob. 4TF Ch. 1.4 - Prob. 5TF Ch. 1.5 - Prob. 1TB Ch. 1.5 - Prob. 2TB Ch. 1.5 - Prob. 0C Ch. 1.5 - Prob. 1C Ch. 1.5 - Prob. 2C Ch. 1.5 - Prob. 3C Ch. 1.5 - Prob. 4C Ch. 1.5 - Prob. 5C Ch. 1.5 - Prob. 6C Ch. 1.5 - Prob. 7C Ch. 1.5 - Prob. 8C Ch. 1.5 - Prob. 9C Ch. 1.5 - Prob. 10C Ch. 1.5 - Prob. 11C Ch. 1.5 - Prob. 12C Ch. 1.5 - Prob. 13C Ch. 1.5 - Prob. 14C Ch. 1.5 - Prob. 15C Ch. 1.5 - Prob. 16C Ch. 1.5 - Prob. 17C Ch. 1.5 - Prob. 18C Ch. 1.5 - Prob. 19C Ch. 1.5 - 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ACP Ch. 1 - Prob. BCP Ch. 1 - Prob. CCP Ch. 1 - Prob. DCP

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The intervals on which function is positive or negative by using the intermediate value theorem and definition of continuity.

Solution Summary: The author explains the intermediate value theorem and definition of continuity to find the intervals on which the functions are positive or negative.

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To find:The intervals on which function is positive or negative by using the intermediate value theorem and definition of continuity.

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Chapter 1 Solutions