Explanation Given : The function is f ( x ) = e 3 x − e 2 x . Calculation: Derivate the function with respect to x as follows: d d x f ( x ) = d d x ( e 3 x − e 2 x ) f ′ ( x ) = 3 e 3 x − 2 e 2 x For increasing interval of the function, f ′ ( x ) > 0 3 e 3 x − 2 e 2 x > 0 x ∈ ( − 0.4 , ∞ ) The sign chart is as follows: For decreasing interval of the function, f ′ ( x ) < 0 3 e 3 x − 2 e 2 x < 0 x ∈ ( − ∞ , − 0.4 ) The sign chart is shown below:

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Chapter 3.3, Problem 78S

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To sketch: The graph of the function f(x)=e3x−e2x .

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Chapter 3.3, Problem 77S

Chapter 3.3, Problem 79S

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Chapter 3 Solutions

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The graph of the function f ( x ) = e 3 x − e 2 x .

Solution Summary: The author illustrates the graph of the function f(x) = e3x-.

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Chapter 3 Solutions