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x 5x+6 Is it differentiable Is f(x) = x2 differentiable at

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

Solution for problem 69AE 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 69AE

x ?5x+6 Is it differentiable?? Is f(x) = x?2 differentiable at x = 2? Justify your answer.

Step-by-Step Solution:
Step 1 of 3

SOLUTION STEP 1 2 (x3)(x2) Given f(x) = x 5x+6= = x 3 x2 x2 STEP 2 We need to find whether f(x)=x-3 is differentiable at x=2. For that ,we consider the left and right hand derivatives of the function at x=2. The left hand derivative of f(x) at x=2 is f(2+h)f(2) f(2) = lim = lim 2+h32+3 = lim h = 1 h2 h h2 h h2 h The right hand derivative of f(x) at x=2 is f(2+h)f(2) 2+h32+3 h f+(2) = lim+ h = lim + h = lim +h = 1 h2 h2 h2 Therefore we have f (2+ = f () Thus the function f(x) is differentiable at x=2. x 5x+6 The graph of f(x) = x2 = x 3 can be drawn as

Step 2 of 3

Chapter 3.1, Problem 69AE 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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x 5x+6 Is it differentiable Is f(x) = x2 differentiable at