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 ( t ) = ( t 3 + 1 ) 2 f ' ( t ) = 2 ( t 3 + 1 ) ( 3 t 2 ) Let f ' ( t ) = 0 Critical points will be t = − 1 , 0 Now, let’s check the sign of derivative of function. Interval ( − ∞ , − 1 ) ( − 1 , 0 ) ( 0 , ∞ ) Sign of f ' ( x ) - + + Interval of increasing is ( − 1 , 0 ) ∪ ( 0

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

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

Publisher: Kendall Hunt Publishing

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Chapter 4.3, Problem 23PS

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Chapter 4.3, Problem 22PS

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Chapter 4 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

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The monotonicity, concavity and graph of f ( t ) = ( t 3 + 1 ) 2

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