To determine To sketch: The graph of the function f ( x ) = ln ( 1 − x ) by using graphing strategy. Explanation Definition used: If f ' ( x ) > 0 on an interval ( a , b ) , then the graph of f ( x ) increases on that interval and if f ' ( x ) < 0 then f ( x ) decreases on that interval. Concavity: For the interval, ( a , b ) , if f ′ ′ ( x ) > 0 , then the function f is concave upward and if f ′ ′ ( x ) < 0 , then f is concave downward. Calculation: The given function is f ( x ) = ln ( 1 − x ) . The domain of the function f ( x ) = ln ( y ) , y > 0 is obtained as follows, y > 0 1 − x > 0 x < 1 So the domain of the function is ( − ∞ , 1 ) Substitute x = 0 for the function to obtain y -intercepts. f ( 0 ) = ln ( 1 ) = 0 The y -intercept of the function is ( 0 , 0 ) . Equate f ( x ) to 0 to obtain its x -intercepts. ln ( 1 − x ) = 0 1 − x = e 0 1 − x = 1 x = 0 Thus, the x -intercept is ( 0 , 0 ) . Since, lim x → ∞ ( ln ( 1 − x ) ) = ∞ , it has no horizontal asymptote The vertical asymptote is obtained as follows, lim x → 1 ( ln ( 1 − x ) ) = − ∞ . That is, as x → 1 , the value of the function f ( x ) = ln ( 1 − x ) tends to infinity. So the vertical asymptote is x = 1 . The derivative of the function f ( x ) is, f ′ ( x ) = d d x ( ln ( 1 − x ) ) = − 1 ( 1 − x ) Equate f ′ ( x ) to 0 to obtain the critical number

College Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

14th Edition

ISBN: 9780134674148

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker

Publisher: PEARSON

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Chapter 11.4, Problem 31E

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To sketch: The graph of the function f(x)=ln(1−x) by using graphing strategy.

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Chapter 11.4, Problem 30E

Chapter 11.4, Problem 32E

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Chapter 11 Solutions

College Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Ch. 11.1 - Matched Problem 1 Repeat Example 1 for f(x) = x2 –...Ch. 11.1 - Matches Problem 2 Find the critical numbers of f,...Ch. 11.1 - Matched Problem 3 Find the critical numbers of f,...Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 7MP Ch. 11.1 - Prob. 8MP Ch. 11.1 - Prob. 9MP Ch. 11.1 - Skills Warm-up Exercises In Problems 1-8, inspect...

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