Explanation Given information: The inequality is 5 x 3 − x 2 − 4 x + 4 < 0 . Calculation: The given inequality is 5 x 3 − x 2 − 4 x + 4 < 0 . Consider the left hand side of the above inequality 5 x 3 − x 2 − 4 x + 4 as r ( x ) and factorize the rational function r ( x ) as, r ( x ) = 5 x 3 − x 2 − 4 x + 4 = 5 x 2 ( x − 1 ) − 4 ( x − 1 ) = 5 ( x − 1 ) ( x 2 − 4 ) = 5 ( x − 1 ) ( x − 2 ) ( x + 2 ) Therefore, the factorized form of the rational function r ( x ) is r ( x ) = 5 ( x − 1 ) ( x − 2 ) ( x + 2 ) . Then the inequality becomes r ( x ) < 0 . The numerator and denominator of the rational function r ( x ) are 5 and ( x − 1 ) ( x − 2 ) ( x + 2 ) respectively. Therefore, the cut points of the rational function r ( x ) are − 2 , 1 and 2 Hence, the intervals determined by the cut points of the rational function r ( x ) are ( − ∞ , − 2 ) , ( − 2 , 1 ) , ( 1 , 2 ) and ( 2 , ∞ ) . The sign of the factors, in each interval are shown in Table 1

7th Edition

ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 3, Problem 97E

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The inequality 5x3−x2−4x+4<0.

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Chapter 3, Problem 96E

Chapter 3, Problem 98E

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