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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4 - Problem 16re
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4 - Problem 16re

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Curve sketching Use the guidelines of this | Ch 4 - 16RE

ISBN: 9780321570567 2

Solution for problem 16RE Chapter 4

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition

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Problem 16RE

Curve sketching Use the guidelines of this chapter to make a complete graph of the following functions on their domains or on the given interval. Use a graphing utility to check your work.

$$f(x)=\frac{x^{2}+x}{4-x^{2}}$$

Step-by-Step Solution:

Solution Step 1 x +x In this problem we need to make a complete graph of f(x) = 4x2in its domain or in the given interval. Since the interval is not mentioned, we take the domain. Here in the given function equate denominator to 0, we get x = ±2, therefore the domain is {x; x = / ±2} . In order to sketch the complete graph, we need to find the critical points, inflection points, local maximum and local minimum if possible. First let us see the definitions: Critical point: An interior point cof the domain of a function f at which f (c) = 0or f(c)fails to exist is called a critical point of f Inflection Point: An inflection point is a point on a curve at which the sign of the curvature (i.e., the concavity) changes. Inflection points may be stationary points, but are not local maxima or local minima. A necessary condition for x to be an inflection point is f (x) = 0 Local maximum: Let f be function defined on an interval [a,b]and let pbe a point in the open interval (a,b). Then the function f has local maximum at pif f(p) f(x) for all xin the neighborhood of the point p. Local minimum: Let f be function defined on an interval [a,b]and let pbe a point in the open interval (a,b). Then the function f has local minimum at pif f(p) f(x)for all x in the neighborhood of the point p.

Step 2 of 6

Step 3 of 6

ISBN: 9780321570567

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: use, graphing, complete, curve, domains. This expansive textbook survival guide covers 112 chapters, and 7700 solutions. The answer to “?Curve sketching Use the guidelines of this chapter to make a complete graph of the following functions on their domains or on the given interval. Use a graphing utility to check your work.$$f(x)=\frac{x^{2}+x}{4-x^{2}}$$” is broken down into a number of easy to follow steps, and 33 words. Since the solution to 16RE from 4 chapter was answered, more than 438 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 16RE from chapter: 4 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM.

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