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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.1 - Problem 8e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 4.1 - Problem 8e

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# Sketch the graph of a function f that has a local minimum

ISBN: 9780321570567 2

## Solution for problem 8E Chapter 4.1

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition

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Problem 8E

Sketch the graph of a fun?ction ?f that has a local minimum value at a point w? ? er? '? )is undefined.

Step-by-Step Solution:
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STEP_BY_STEP SOLUTION Step-1 be defined on the interval [a,b] , and x be0the interior 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 a0e all less than f(x ). 0 That is , f(x) f(x 0Let f Thus, the graph of f nea r x has a peak at x . 0 0 A function f has a local minimum or relative minimum at a point x if th0 values f(x) of f for x ‘near’ x a0 re all greater than f(0 ) . That is f(x) f(x ). 0 Thus, the graph of f near x h0s a trough at x . (T0 make the distinction clear, sometimes the ‘plain’ maximum and minimum are called absolute maximum and minimum). Step_2 Let f be a continuous function defined on an open interval containing a number ‘c’.The number ‘c’ is critical value ( or critical number ). If f (c) = 0 1 or f (c) is undefined. A critical point on that graph of f has the form (c,f(c)). Step-3 Example-1 Graph of the given data is ; The given function is y = f(x) =|x| = { x , if x 0 = { -x , if x<0. 1 Here f (x) is does not exist , since left hand derivative is -1 , and right hand derivative is 1. But , the function attains the local minimum at x=0. Example-2 In the given graph it is clear that the function is continuous . The function has local minimum at x= c , and at ‘c’ , f (x) does not exist.

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##### ISBN: 9780321570567

The full step-by-step solution to problem: 8E from chapter: 4.1 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. The answer to “Sketch the graph of a fun?ction ?f that has a local minimum value at a point w? ? er? '? )is undefined.” is broken down into a number of easy to follow steps, and 22 words. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. Since the solution to 8E from 4.1 chapter was answered, more than 416 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This full solution covers the following key subjects: ction, Fun, graph, local, minimum. This expansive textbook survival guide covers 85 chapters, and 5218 solutions.

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