Explanation Given information: The function is f ( x ) = ( x 2 − 9 ) 2 . Calculation: Consider the function. f ( x ) = ( x 2 − 9 ) 2 Hence, there are no vertical and horizontal asymptote. Differentiate the function. f ′ ( x ) = 2 ( x 2 − 9 ) ( 2 x ) = 4 x ( x 2 − 9 ) Hence, the function is increasing for all − 3 < x < 0 , x > 3 and decreasing for x < − 3 , 0 < x < 3 . Differentiate above equation. f ″ ( x ) = 4 ( x 2 − 9 ) + 4 x ( 2 x ) = 12 (

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Chapter 4.4, Problem 33PS

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To explain: The point where the graph of given function is rising, falling, the concavity, the point of inflection and vertical and horizontal asymptotes.

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Chapter 4.4, Problem 32PS

Chapter 4.4, Problem 34PS

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Consider the graphs of y = f(x) and y = g(x) in the given diagram y= f(x). y = g(x) Evaluate (f+g)(2) -5 Determine all for which g(x) < f(x) Determine all for which f(x) +3 = g(x)

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Chapter 4 Solutions

Calculus

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The point where the graph of given function is rising, falling, the concavity, the point of inflection and vertical and horizontal asymptotes.

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Chapter 4 Solutions