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# Solution: Graphing rational functions Use the guidelines of

ISBN: 9780321570567 2

## Solution for problem 19E Chapter 4.3

Calculus: Early Transcendentals | 1st Edition

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Problem 19E

Graphing rational functions ?Use the guidelines of this section to make a complete graph of f.

Step-by-Step Solution:
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Solution:- Step1 Given function is x +12 f(x)= 2x+1 The zero of the denominator is x=-0.5 so, the domain is { x; x= / -0.5} This function consists of an even function divided by an odd function. The product of even and odd function is odd. Therefore, the graph is symmetric about the origin. Step2 Differentiate the given equation to find f’(x) we get, 2(x +12) f’(x)= 2x - 2 2x+1 (2x+1) 2x(2x+1)2(x +12) = (2x8) = 4x1642+6 (2x+1) 4x +2x2x 24 = (2x+1) 2 = 2x +2x24 (2x+1) Again differentiate f’(x) to find f’’(x) we get, f’’(x)=(4x+2)/(2x+1)^2 - (4(2x^2+2x-24))/(2x+1)^3 = ((4x+2)(2x+1)-8x^2-8x+96)/(2x+1)^3 = (8x^2+4x+4x+2-8x^2-8x+96)/(2x+1)^3 = 98/(2x+1)^3 Step3 To get extreme values we have to use f’(x)=0 => (2(x^2+x-12))/(2x+1)^2 =0 =>2(x^2+x-12)=0 => x^2+x-12=0 =>x^2+4x-3x-12=0 => x(x+4)-3(x+4)=0 =>(x-3)(x+4)=0 =>x=3,-4 Critical points are 3,-4 Step4...

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##### ISBN: 9780321570567

The answer to “Graphing rational functions ?Use the guidelines of this section to make a complete graph of f.” is broken down into a number of easy to follow steps, and 16 words. Since the solution to 19E from 4.3 chapter was answered, more than 325 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 19E from chapter: 4.3 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: complete, functions, graph, graphing, guidelines. This expansive textbook survival guide covers 85 chapters, and 5218 solutions.

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