Explanation Let f ( x ) be a continuous function on [a, b] and differentiable in (a, b) then f ( x ) is increasing in [ a , b ] if f ' ( x ) > 0 for each x ∈ ( a , b ) f ( x ) is decreasing in [ a , b ] if f ' ( x ) < 0 for each x ∈ ( a , b ) f ( u ) = 3 u 4 − 4 u 3 − 12 u 2 + 18 u − 5 f ' ( u ) = 12 u 3 − 12 u 2 − 24 u + 18 Let f ' ( u ) = 0 Critical points will be x = -1 .33641 , 0 .67596 , 1 .66044 Now, let’s check the sign of derivative of function. Interval ( − ∞ , -1 .33641 ) ( 1 .33641 , 0 .67596 ) ( 0 .67596 , 1 .66044 ) ( 1 .66044 , ∞ ) Sign of f ' ( x ) - + - + Interval of increasing is ( 1 .33641 , 0 .67596 ) ∪ ( 1 .66044 , ∞ ) Interval of decreasing is ( − ∞ , -1

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Question

Chapter 4.3, Problem 20PS

To determine

The monotonicity, concavity and graph of f(u)=3u4−4u3−12u2+18u−5

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Chapter 4.3, Problem 19PS

Chapter 4.3, Problem 21PS

Chapter 4 Solutions

Calculus

Ch. 4.1 - Prob. 1PS Ch. 4.1 - Prob. 2PS Ch. 4.1 - Prob. 3PS Ch. 4.1 - Prob. 4PS Ch. 4.1 - Prob. 5PS Ch. 4.1 - Prob. 6PS Ch. 4.1 - Prob. 7PS Ch. 4.1 - Prob. 8PS Ch. 4.1 - Prob. 9PS Ch. 4.1 - Prob. 10PS

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The monotonicity, concavity and graph of f ( u ) = 3 u 4 − 4 u 3 − 12 u 2 + 18 u − 5

Solution Summary: The author explains the monotonicity, concavity and graph of f(u)=3u44u312u2+18u5 Interval of increasing is (1.33641,0.6

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The monotonicity, concavity and graph of f(u)=3u4−4u3−12u2+18u−5

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