Explanation Use online graphing calculator and obtain the graph of f ( x ) = x 3 + 1 x 6 + 1 as shown in below Figure 1. In the above graph the point ( − 1.304 , − 0.206 ) is a point of local minima and ( 0.745 , 1.207 ) is a point of local maxima . Also graph shows that the line y = 0 is horizontal asymptote. Differentiate the given function with respect to x . f ( x ) = x 3 + 1 x 6 + 1 f ′ ( x ) = ( x 6 + 1 ) ( 3 x 2 ) − ( x 3 + 1 ) ( 6 x 5 ) ( x 6 + 1 ) 2 = 3 x 2 − 3 x 8 + 6 x 5 ( x 6 + 1 ) 2 Therefore, f ′ ( x ) = 3 x 2 − 3 x 8 + 6 x 5 ( x 6 + 1 ) 2 . Plot the graph for f ′ ( x ) with the help of online graphing calculator as shown in below Figure 2. From the graph observe that function is increasing on the interval ( − 1.087 , − 0.543 ) , ( 0 , 0.822 ) and ( 1.637 , ∞ ) and decreasing elsewhere.. Now differentiate first derivative again with respect to x

Single Variable Calculus: Early Transcendentals, Volume I

8th Edition

ISBN: 9781305270343

Author: James Stewart

Publisher: Cengage Learning

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Chapter 4, Problem 36RE

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To sketch: The graph of f(x)=x3+1x6+1 such that all the important aspects of the graphs are visible.

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Chapter 4, Problem 35RE

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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 f ( x ) = x 3 + 1 x 6 + 1 such that all the important aspects of the graphs are visible.

Solution Summary: The author illustrates how to plot the graph of f(x)=x 3+1 x.

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To sketch: The graph of f(x)=x3+1x6+1 such that all the important aspects of the graphs are visible.

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Chapter 4 Solutions