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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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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 x +x check your work. f(x) = 4?x2

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 Given f(x) = x +x 4x2 Since this function consists of even function divided by even function, and we know that the product of even and even function is even. Therefore the graph is symmetric about origin. Now let us find the critical points. 2 Consider f(x) = 4xx2 x +8x+4 Thus f (x) = (4x ) Now by the definition of critical points given in step 1, we equate f’(x) to 0. f(x) = 0 Thus the critical points are x = 0.5359, 7.4641 Step 3 Now let us find the inflection points. By definition the necessary condition is f (x) = 0 We have f (x) = x +8x+4 (4x )2 Now f (x) = 0, we get

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##### 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 85 chapters, and 5218 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 x +x check your work. f(x) = 4?x2” is broken down into a number of easy to follow steps, and 38 words. Since the solution to 16RE from 4 chapter was answered, more than 323 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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