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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.1 - Problem 20e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.1 - Problem 20e

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# Designing a function S ketch the graph of a continuous

ISBN: 9780321570567 2

## Solution for problem 20E Chapter 4.1

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition

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Problem 20E

Designing a function S ? ketch the graph of a continuous function ? f on [0, 4] ?satisfying the given properties. ? ? f?(? )?= 0 for ? =1, 2,? and 3; f? has an absolute minim ? um a ? t ?x = ? has no local extre?mum at ?x = ? 2; and f ? has an absolute maxi?mum at x ? =3.

Step-by-Step Solution:
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STEP_BY_STEP SOLUTION Step_1 When an output value of a function is a maximum or a minimum over the entire domain of the function, the value is called the absolute maximum or the absolute minimum. Let f be a function with domain D and let c be a fixed c onstant in D. Then the o utput value ) is the 1. Absolute maximum value of f on D if and only if f(x) f(c) , for all x in D. 2. Absolute minimum value of f on D if and only if f(c) f(x) , for all x in D. Step-2 Let f be defined on the interval [a,b] , and x be the 0nterior point on [a,b]. A function f has a local maximum or relative maximum at a point x if the values 0 f(x) of f for x ‘near’ x are all less than f(x ). 0 0 That is , f(x) f(x ) 0 Thus, the grap h of f near x ha0 a p eak at x 0 A function f has a local minimum or relative minimum at a point x if the values0 f(x) of f for x ‘near’ x a 0 re all greater than f(x )0 . That is f(x) f(x ).0 Thus, the graph of f near x has a trough at x . (To make the distinction clear, 0 0 sometimes the ‘plain’ maximum and minimum are called absolute maximum and minimum). Step_3 Given is ; 1 ‘f’ be a continuous function on [0,4] , and given properties are ; f (x) = 0 , for x=1 , 2 and 3, f has an absolute maximum at x=3 , an absolute minimum at x=1, and f has no local extreme values at x=2. Now , we need to sketch the graph of f(x) on [0,4]. Step-4 Let , ‘f’ be a continuous function on [0,4] . so, the graph of f(x) is continuous on [0,4].From the given it is clear that 0, 4 are the endpoints of the interval , and 1,2 ,3are the interior points on the interval. 1 Given ; f (x) = 0 , for x= 1 , 2 and 3 .so the graph of f(x) has slope is zero at x=1, 2 ,3, and also given that ; f has an absolute maximum at x=3 , so f(3) f(x) for all x in [0,4].That is f(3) is an absolute maximum value at x= 3, since from the definition step-1. f has an absolute minimum at x=1 , so f(x) f(1) for all x in [0,4].That is f(1) is an absolute minimum value at x=1, since from the definition step-1. f has no local extreme values at x=2 .So , at x=2 the graph of f has no local maximum and no local minimum value. Step-5 Therefore , the related graph of the function y = f(x) is ;

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##### ISBN: 9780321570567

This full solution covers the following key subjects: absolute, mum, function, ketch, designing. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The answer to “Designing a function S ? ketch the graph of a continuous function ? f on [0, 4] ?satisfying the given properties. ? ? f?(? )?= 0 for ? =1, 2,? and 3; f? has an absolute minim ? um a ? t ?x = ? has no local extre?mum at ?x = ? 2; and f ? has an absolute maxi?mum at x ? =3.” is broken down into a number of easy to follow steps, and 65 words. The full step-by-step solution to problem: 20E from chapter: 4.1 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. Since the solution to 20E from 4.1 chapter was answered, more than 315 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1.

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