Explanation Definition used: Increasing/Decreasing Test: “(a) If f ′ ( x ) > 0 on an interval, then f is increasing on that interval. (b) If f ′ ( x ) < 0 on an interval, then f is decreasing on that interval”. Concavity Test: “(a) If f ′ ′ ( x ) > 0 for all x in I , then the graph of f is concave upward on I . (b) If f ′ ′ ( x ) < 0 for all x in I , then the graph of f is concave downward on I”. Vertical asymptote x = 0 means that the graph of f ( x ) approaches infinity from either side near the point at x = 0 but not exactly at x = 0 . The condition f ′ ( x ) > 0 if x < − 2 indicates that f is increasing on ( − ∞ , − 2 )

Single Variable Calculus: Early Transcendentals, Volume I

8th Edition

ISBN: 9781305270343

Author: James Stewart

Publisher: Cengage Learning

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Chapter 4.3, Problem 26E

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To sketch: The graph of the function which satisfy the following conditions that

vertical asymptote x=0 , f′(x)>0 if x<−2 , f′(x)<0 if x>−2 (x≠0) , f′′(x)<0 if x<0 , f′′(x)>0 if x>0 .

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Chapter 4.3, Problem 25E

Chapter 4.3, Problem 27E

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Chapter 4 Solutions

Single Variable Calculus: Early Transcendentals, Volume I

Ch. 4.1 - Explain the difference between an absolute minimum...Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Use the graph to state the absolute and local...Ch. 4.1 - Use the graph to state the absolute and local...Ch. 4.1 - Sketch the graph of a function f that is...Ch. 4.1 - Sketch the graph of a function f that is...Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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The graph of the function which satisfy the following conditions that vertical asymptote x = 0 , f ′ ( x ) > 0 if x < − 2 , f ′ ( x ) < 0 if x > − 2 ( x ≠ 0 ) , f ′ ′ ( x ) < 0 if x < 0 , f ′ ′ ( x ) > 0 if x > 0 .

Solution Summary: The author illustrates the graph of the function which satisfy the following conditions: vertical asymptote x=0 and concavity test.

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To sketch: The graph of the function which satisfy the following conditions that

vertical asymptote x=0 , f′(x)>0 if x<−2 , f′(x)<0 if x>−2 (x≠0) , f′′(x)<0 if x<0 , f′′(x)>0 if x>0 .

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Chapter 4 Solutions

The graph of the function which satisfy the following conditions that vertical asymptote x = 0 , f ′ ( x ) &gt; 0 if x &lt; − 2 , f ′ ( x ) &lt; 0 if x &gt; − 2 ( x ≠ 0 ) , f ′ ′ ( x ) &lt; 0 if x &lt; 0 , f ′ ′ ( x ) &gt; 0 if x &gt; 0 .

Solution Summary: The author illustrates the graph of the function which satisfy the following conditions: vertical asymptote x=0 and concavity test.

Concept explainers

Videos

To sketch: The graph of the function which satisfy the following conditions that vertical asymptote x=0 , f′(x)>0 if x<−2 , f′(x)<0 if x>−2 (x≠0) , f′′(x)<0 if x<0 , f′′(x)>0 if x>0 .

Want to see the full answer?

Chapter 4 Solutions

The graph of the function which satisfy the following conditions that vertical asymptote x = 0 , f ′ ( x ) > 0 if x < − 2 , f ′ ( x ) < 0 if x > − 2 ( x ≠ 0 ) , f ′ ′ ( x ) < 0 if x < 0 , f ′ ′ ( x ) > 0 if x > 0 .

To sketch: The graph of the function which satisfy the following conditions that

vertical asymptote x=0 , f′(x)>0 if x<−2 , f′(x)<0 if x>−2 (x≠0) , f′′(x)<0 if x<0 , f′′(x)>0 if x>0 .