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# Solved: Graphing rational functions Use the guidelines of ## Problem 15E Chapter 4.3

Calculus: Early Transcendentals | 1st Edition

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Problem 15E

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

Step-by-Step Solution:
Step 1 of 3

Solution: Step1 Given function is f(x)=x^2/x-2 The zero of the denominator is x=2 so, the domain is { x; x/ 2} 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, f’(x)= x/(x-2) - x^2/(x-2)^2 = (2x(x-2)-x^2)/(x-2)^2 = (2x^2-4x-x^2)/(x-2)^2 = (x^2-4x)/(x-2)^2 = (x-4)x/(x-2)^2 Again differentiate f’(x) to find f’’(x) we get, f’’(x)=x/(x-2)^2- 2x(x-4)/(x-2)^3+(x-4)/(x-2)^2 = (x(x-2)-2x(x-4)+(x-4)(x-2))/(x-2)^3 = (x^2-2x-2x^2+8x+x^2-6x+8)/(x-2)^3 = 8/(x-2)^3 Step3 To get extreme values we have to use f’(x)=0 => (x-4)x/(x-2)^2 =0 =>(x-4)x=0 => x-4=0, x=0 =>x=4,0 Critical points are 4,0 Step4 To find...

Step 2 of 3

Step 3 of 3

##### ISBN: 9780321570567

The full step-by-step solution to problem: 15E from chapter: 4.3 was answered by Sieva Kozinsky, our top Calculus solution expert on 03/03/17, 03:45PM. Calculus: Early Transcendentals was written by Sieva Kozinsky and is associated to the ISBN: 9780321570567. Since the solution to 15E from 4.3 chapter was answered, more than 254 students have viewed the full step-by-step answer. 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. This full solution covers the following key subjects: complete, functions, graph, graphing, guidelines. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1.

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