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More graphing Make a complete graph of the | Ch 4.3 - 29E

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 29E Chapter 4.3

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 29E

More graphing ?Make a complete graph of the following functions. If an interval is not specified, graph the function on its domain. Use a graphing utility to check your work. f?(?x?)? ? ln. ?X

Step-by-Step Solution:
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Solution:- Step1 Given function is f(x)= x In x And the domain of given function is [0, ] The given function is not an even function and not an odd function. So, the given function is not symmetrical about x-axis and y-axis. Step2 Differentiate the given equation to find f’(x) we get, f’(x)= In(x)+1 Again differentiate f’(x) to find f”(x) we get, 1 f”(x)= x Step3 To get extreme value we have to use f’(x)=0 In(x) + 1=0 In(x)=-1 x=e = 1 1 e 1 x= e is the critical point. Step4 To find the inflection points we have to use f”(x)=0 x=0 1=0 inflection point is not possible. Step5 We have to find increasing, decreasing and concavity 1 x= e is the critical point. Therefore in between ( ,) the function f(x) is increasing and (0, ) it is decreasing. e e Let f”(x)>0 1 >0 x The function is concave upwards if x>0. Step6 Extreme values and inflection points. The inflection points are at 1 f”(x)= x f”( )= 1=e>0 e e 1 Therefore at x= e f(x) has minimum value . Step7 Asymptotes and end behavior Let f’(x)=0 if x= 1 e 1 At x= e then tangent parallel to x- axis limf(x)=lim x In x= 0 x0 x0 xm f(x)=xm x In x= Intercepts At x=0 y=0 If y=0 x= 1 and 0 Step8 Graph of given equation

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Chapter 4.3, Problem 29E is Solved
Step 3 of 3

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

The full step-by-step solution to problem: 29E from chapter: 4.3 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. The answer to “More graphing ?Make a complete graph of the following functions. If an interval is not specified, graph the function on its domain. Use a graphing utility to check your work. f?(?x?)? ? ln. ?X” is broken down into a number of easy to follow steps, and 34 words. Since the solution to 29E from 4.3 chapter was answered, more than 389 students have viewed the full step-by-step answer. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This full solution covers the following key subjects: graph, graphing, interval, function, functions. This expansive textbook survival guide covers 85 chapters, and 5218 solutions.

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More graphing Make a complete graph of the | Ch 4.3 - 29E