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# Answer: More graphing Make a complete graph of the

ISBN: 9780321570567 2

## Solution for problem 28E Chapter 4.3

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition

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Problem 28E

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? ? = (ln?x?)/?x?2

Step-by-Step Solution:
Step 1 of 3

Solution:- Step1 Given function is In x f(x)= x And the domain of given function is [0, ] The given function is not symmetrical about x-axis and y-axis. Step2 Differentiate the given equation to find f’(x) we get, 1 2 In(x) f’(x)= x3 - x3 12 In(x) = x3 Again differentiate f’(x) to find f”(x) we get, f”(x)= 3(12In (x))- 2 x4 x4 3(12In (x))2 3+6In(x)2 6In(x)5 = x4 = x4 = x4 Step3 To get extreme value we have to use f’(x)=0 12 In(x) x =0 1-2In x=0 In x= 1 2 1 x=e 2 1 x=e is the critical point. Step4 To find the inflection points we have to use f”(x)=0 6In4x)=0 x 6 In(x)-5=0 In x= 5 6 6 x=e 6 x=e is the inflection point. Step5 We have to find increasing, decreasing and concavity 1 2 x=e is the critical point. 1 1 Therefore in between (0,e ) the function f(x) is increasing and (e ,) it is decreasing.2 5 x=e is inflection point. 6 6 The function (0,e ) is concave upwards and (e ,) concave down wards. Step6 Extreme values and inflection points. The inflection points are at 6In(x)5 f”(x)= x 1 2 2 6In(e )5 f”(e )= 14 (e ) 523 = 2 <0 e e 1 Therefore at x=e f(x) has maximum value and minimum value does not exist. Step7 Asymptotes and end behavior 1 Let f’(x)=0 if x=e 2 1 At x=e , then tangent parallel to x- axis In x limf(x)=lim x2 = x0 x0 Intercepts At x=0 y= If y=0 x= 1 Step8 Graph of given equation

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##### ISBN: 9780321570567

The full step-by-step solution to problem: 28E 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? ? = (ln?x?)/?x?2” is broken down into a number of easy to follow steps, and 34 words. 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. Since the solution to 28E from 4.3 chapter was answered, more than 406 students have viewed the full step-by-step answer. 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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Answer: More graphing Make a complete graph of the