(a) Explanation Given: A function with a local minimum at x = 3 that is continuous but is not differentiable at x = 3 Calculation: Consider f ( x ) = x − 3 For continuity test; lim x → 3 f ( x ) = lim x → 3 x − 3 = 3 − 3 = 0 = 0 f ( 3 ) = 3 − 3 = 0 Therefore, &em (b) To determine A function having a local maximum at x = -2 that is not differentiable at x = -2 because of removable discontinuity (c) To determine A function having a local minimum at x = 1 that is not differentiable at x =1 because of jump discontinuity.

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 3.1, Problem 2C

(a)

To determine

A function with a local minimum at x = 3 that is continuous but is not differentiable at x = 3

(b)

To determine

A function having a local maximum at x = -2 that is not differentiable at x = -2 because of removable discontinuity

(c)

To determine

A function having a local minimum at x = 1 that is not differentiable at x =1 because of jump discontinuity.

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Chapter 3.1, Problem 1C

Chapter 3.1, Problem 3C

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A function with a local minimum at x = 3 that is continuous but is not differentiable at x = 3

Solution Summary: The author explains that a local minimum at x = 3 is continuous, but not differentiable, because of removable discontinuity.

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A function with a local minimum at x = 3 that is continuous but is not differentiable at x = 3

A function having a local maximum at x = -2 that is not differentiable at x = -2 because of removable discontinuity

A function having a local minimum at x = 1 that is not differentiable at x =1 because of jump discontinuity.

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