Explanation Given information: The function is f ( x ) = x − a x . Definition used: For any function f , a point p in the domain of f where f ' ( p ) = 0 or f ' ( p ) is undefined is called a critical point of the function. Calculation: f ( x ) = x − a x f (Given) Differentiating with respect to ‘t’, we have f ' ( x ) = 1 − a 2 x Equating f ' ( x ) = 0 to find critical points To determine (b) To find: The value of a at the critical point x = 5 and whether f ( x ) has a local minimum or local maximum at this critical point.

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Question

Chapter 4.1, Problem 53P

To determine

(a)

To find:

All critical points of f(x)=x−ax for a positive constant a.

To determine

(b)

To find:

The value of a at the critical point x=5 and whether f(x) has a local minimum or local maximum at this critical point.

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Chapter 4.1, Problem 52P

Chapter 4.1, Problem 54P

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Chapter 4 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

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(a) To find: All critical points of f ( x ) = x − a x for a positive constant a.

Solution Summary: The author explains how to find all critical points of f(x)=x-asqrtx for a positive constant.

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(a)

To find:

All critical points of f(x)=x−ax for a positive constant a.

(b)

To find:

The value of a at the critical point x=5 and whether f(x) has a local minimum or local maximum at this critical point.

Want to see the full answer?

Chapter 4 Solutions

(a) To find: All critical points of f ( x ) = x − a x for a positive constant a.

Solution Summary: The author explains how to find all critical points of f(x)=x-asqrtx for a positive constant.

Concept explainers

Videos

(a) To find: All critical points of f(x)=x−ax for a positive constant a.

(b) To find: The value of a at the critical point x=5 and whether f(x) has a local minimum or local maximum at this critical point.

Want to see the full answer?

Chapter 4 Solutions

(a)

To find:

All critical points of f(x)=x−ax for a positive constant a.

(b)

To find:

The value of a at the critical point x=5 and whether f(x) has a local minimum or local maximum at this critical point.