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Solved: Derivatives from graphs Use the graph of f to

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 40E Chapter 3.1

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 40E

Derivatives from graphs? ?Use the graph of f to sketch a grap ? h of f?.

Step-by-Step Solution:
Step 1 of 3

SOLUTION The objective is to use the graph of f sketch a graph of f . STEP 1 The graph consists of line segments which are the tangent lines. Now to find the slope of the tangent line ,select any 2 points on the line. The slope of a line never changes,so we are free to choose any 2 points. y y Now substitute the points on the equation of slope m = x x1. 2 1 Thus,since it is a tangent line ,the slope of the line is itself the derivative. Now,let the 2 points on the line x < 1 be (1,5) and (-1,1). Substitute the points in the equation of the slope Then we get , 15 4 slope m = 11 = 2 = 2 Therefore the slope of the curve y=f(x) for x<1 is 2.ie f (x) = 2 for x < 1 Similarly, The slope of the curve y = f(x) for x > 1 is -1. ie f(x) =1 for x > 1 STEP 3 Using the above information sketch a graph of f At x=1 the slope of the line changes.So the derivative is undefined and the graph is discontinuous at the point x=1.

Step 2 of 3

Chapter 3.1, Problem 40E is Solved
Step 3 of 3

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Solved: Derivatives from graphs Use the graph of f to