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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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 4.1, Problem 56P

To determine

(a)

To graph:

f(x)=x3−ax for three different values of a.

To determine

(b)

To describe:

The critical points of f and its appearance as a increases.

To determine

(c)

To find:

A formula for the x-coordinates of the critical points of f in terms of a.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Chapter 4.1, Problem 55P

Chapter 4.1, Problem 57P

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Chapter 4 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

Ch. 4.1 - Prob. 1P Ch. 4.1 - Prob. 2P Ch. 4.1 - Prob. 3P Ch. 4.1 - Prob. 4P Ch. 4.1 - Prob. 5P Ch. 4.1 - Prob. 6P Ch. 4.1 - Prob. 7P Ch. 4.1 - Prob. 8P Ch. 4.1 - Prob. 9P Ch. 4.1 - Prob. 10P

Ch. 4.1 - Prob. 11P Ch. 4.1 - Prob. 12P Ch. 4.1 - Prob. 13P Ch. 4.1 - Prob. 14P Ch. 4.1 - Prob. 15P Ch. 4.1 - Prob. 16P Ch. 4.1 - Prob. 17P Ch. 4.1 - Prob. 18P Ch. 4.1 - Prob. 19P Ch. 4.1 - Prob. 20P Ch. 4.1 - Prob. 21P Ch. 4.1 - Prob. 22P Ch. 4.1 - Prob. 23P Ch. 4.1 - Prob. 24P Ch. 4.1 - Prob. 25P Ch. 4.1 - Prob. 26P Ch. 4.1 - Prob. 27P Ch. 4.1 - Prob. 28P Ch. 4.1 - Prob. 29P Ch. 4.1 - Prob. 30P Ch. 4.1 - Prob. 31P Ch. 4.1 - Prob. 32P Ch. 4.1 - Prob. 33P Ch. 4.1 - Prob. 34P Ch. 4.1 - Prob. 35P Ch. 4.1 - Prob. 36P Ch. 4.1 - Prob. 37P Ch. 4.1 - Prob. 38P Ch. 4.1 - Prob. 39P Ch. 4.1 - Prob. 40P Ch. 4.1 - Prob. 41P Ch. 4.1 - Prob. 42P Ch. 4.1 - Prob. 43P Ch. 4.1 - Prob. 44P Ch. 4.1 - Prob. 45P Ch. 4.1 - Prob. 46P Ch. 4.1 - Prob. 47P Ch. 4.1 - Prob. 48P Ch. 4.1 - Prob. 49P Ch. 4.1 - Prob. 50P Ch. 4.1 - Prob. 51P Ch. 4.1 - Prob. 52P Ch. 4.1 - Prob. 53P Ch. 4.1 - Prob. 54P Ch. 4.1 - Prob. 55P Ch. 4.1 - Prob. 56P Ch. 4.1 - Prob. 57P Ch. 4.1 - Prob. 58P Ch. 4.2 - Prob. 1P Ch. 4.2 - Prob. 2P Ch. 4.2 - Prob. 3P Ch. 4.2 - Prob. 4P Ch. 4.2 - Prob. 5P Ch. 4.2 - Prob. 6P Ch. 4.2 - Prob. 7P Ch. 4.2 - Prob. 8P Ch. 4.2 - Prob. 9P Ch. 4.2 - Prob. 10P Ch. 4.2 - Prob. 11P Ch. 4.2 - Prob. 12P Ch. 4.2 - Prob. 13P Ch. 4.2 - Prob. 14P Ch. 4.2 - Prob. 15P Ch. 4.2 - Prob. 16P Ch. 4.2 - Prob. 17P Ch. 4.2 - Prob. 18P Ch. 4.2 - Prob. 19P Ch. 4.2 - Prob. 20P Ch. 4.2 - Prob. 21P Ch. 4.2 - Prob. 22P Ch. 4.2 - Prob. 23P Ch. 4.2 - Prob. 24P Ch. 4.2 - Prob. 25P Ch. 4.2 - Prob. 26P Ch. 4.2 - Prob. 27P Ch. 4.2 - Prob. 28P Ch. 4.2 - Prob. 29P Ch. 4.2 - Prob. 30P Ch. 4.2 - Prob. 31P Ch. 4.2 - Prob. 32P Ch. 4.2 - Prob. 33P Ch. 4.2 - Prob. 34P Ch. 4.2 - Prob. 35P Ch. 4.2 - Prob. 36P Ch. 4.2 - Prob. 37P Ch. 4.2 - Prob. 38P Ch. 4.2 - Prob. 39P Ch. 4.2 - Prob. 40P Ch. 4.2 - Prob. 41P Ch. 4.3 - Prob. 1P Ch. 4.3 - Prob. 2P Ch. 4.3 - Prob. 3P Ch. 4.3 - Prob. 4P Ch. 4.3 - Prob. 5P Ch. 4.3 - Prob. 6P Ch. 4.3 - Prob. 7P Ch. 4.3 - Prob. 8P Ch. 4.3 - Prob. 9P Ch. 4.3 - Prob. 10P Ch. 4.3 - Prob. 11P Ch. 4.3 - Prob. 12P Ch. 4.3 - Prob. 13P Ch. 4.3 - Prob. 14P Ch. 4.3 - Prob. 15P Ch. 4.3 - Prob. 16P Ch. 4.3 - Prob. 17P Ch. 4.3 - Prob. 18P Ch. 4.3 - Prob. 19P Ch. 4.3 - Prob. 20P Ch. 4.3 - Prob. 21P Ch. 4.3 - Prob. 22P Ch. 4.3 - Prob. 23P Ch. 4.3 - Prob. 24P Ch. 4.3 - Prob. 25P Ch. 4.3 - Prob. 26P Ch. 4.3 - Prob. 27P Ch. 4.3 - Prob. 28P Ch. 4.3 - Prob. 29P Ch. 4.3 - Prob. 30P Ch. 4.3 - Prob. 31P Ch. 4.3 - Prob. 32P Ch. 4.3 - Prob. 33P Ch. 4.3 - Prob. 34P Ch. 4.3 - Prob. 35P Ch. 4.3 - Prob. 36P Ch. 4.3 - Prob. 37P Ch. 4.3 - Prob. 38P Ch. 4.3 - Prob. 39P Ch. 4.3 - Prob. 40P Ch. 4.3 - Prob. 41P Ch. 4.3 - Prob. 42P Ch. 4.3 - Prob. 43P Ch. 4.3 - Prob. 44P Ch. 4.3 - Prob. 45P Ch. 4.3 - Prob. 46P Ch. 4.3 - Prob. 47P Ch. 4.3 - Prob. 48P Ch. 4.3 - Prob. 49P Ch. 4.3 - Prob. 50P Ch. 4.3 - Prob. 51P Ch. 4.3 - Prob. 52P Ch. 4.3 - Prob. 53P Ch. 4.3 - Prob. 54P Ch. 4.3 - Prob. 55P Ch. 4.3 - Prob. 56P Ch. 4.3 - Prob. 57P Ch. 4.3 - Prob. 58P Ch. 4.3 - Prob. 59P Ch. 4.3 - Prob. 60P Ch. 4.4 - Prob. 1P Ch. 4.4 - Prob. 2P Ch. 4.4 - Prob. 3P Ch. 4.4 - Prob. 4P Ch. 4.4 - Prob. 5P Ch. 4.4 - Prob. 6P Ch. 4.4 - Prob. 7P Ch. 4.4 - Prob. 8P Ch. 4.4 - Prob. 9P Ch. 4.4 - Prob. 10P Ch. 4.4 - Prob. 11P Ch. 4.4 - Prob. 12P Ch. 4.4 - Prob. 13P Ch. 4.4 - Prob. 14P Ch. 4.4 - Prob. 15P Ch. 4.4 - Prob. 16P Ch. 4.4 - Prob. 17P Ch. 4.4 - Prob. 18P Ch. 4.4 - Prob. 19P Ch. 4.4 - Prob. 20P Ch. 4.4 - Prob. 21P Ch. 4.4 - Prob. 22P Ch. 4.4 - Prob. 23P Ch. 4.4 - Prob. 24P Ch. 4.4 - Prob. 25P Ch. 4.4 - Prob. 26P Ch. 4.4 - Prob. 27P Ch. 4.4 - Prob. 28P Ch. 4.4 - Prob. 29P Ch. 4.4 - Prob. 30P Ch. 4.4 - Prob. 31P Ch. 4.4 - Prob. 32P Ch. 4.4 - Prob. 33P Ch. 4.4 - Prob. 34P Ch. 4.4 - Prob. 35P Ch. 4.5 - Prob. 1P Ch. 4.5 - Prob. 2P Ch. 4.5 - Prob. 3P Ch. 4.5 - Prob. 4P Ch. 4.5 - Prob. 5P Ch. 4.5 - Prob. 6P Ch. 4.5 - Prob. 7P Ch. 4.5 - Prob. 8P Ch. 4.5 - Prob. 9P Ch. 4.5 - Prob. 10P Ch. 4.5 - Prob. 11P Ch. 4.5 - Prob. 12P Ch. 4.5 - Prob. 13P Ch. 4.5 - Prob. 14P Ch. 4.5 - Prob. 15P Ch. 4.5 - Prob. 16P Ch. 4.5 - Prob. 17P Ch. 4.6 - Prob. 1P Ch. 4.6 - Prob. 2P Ch. 4.6 - Prob. 3P Ch. 4.6 - Prob. 4P Ch. 4.6 - Prob. 5P Ch. 4.6 - Prob. 6P Ch. 4.6 - Prob. 7P Ch. 4.6 - Prob. 8P Ch. 4.6 - Prob. 9P Ch. 4.6 - Prob. 10P Ch. 4.6 - Prob. 11P Ch. 4.6 - Prob. 12P Ch. 4.6 - Prob. 13P Ch. 4.6 - Prob. 14P Ch. 4.6 - Prob. 15P Ch. 4.6 - Prob. 16P Ch. 4.6 - Prob. 17P Ch. 4.6 - Prob. 18P Ch. 4.6 - Prob. 19P Ch. 4.6 - Prob. 20P Ch. 4.6 - Prob. 21P Ch. 4.6 - Prob. 22P Ch. 4.6 - Prob. 23P Ch. 4.6 - Prob. 24P Ch. 4.6 - Prob. 25P Ch. 4.6 - Prob. 26P Ch. 4.6 - Prob. 27P Ch. 4.6 - Prob. 28P Ch. 4.6 - Prob. 29P Ch. 4.6 - Prob. 30P Ch. 4.6 - Prob. 31P Ch. 4.7 - Prob. 1P Ch. 4.7 - Prob. 2P Ch. 4.7 - Prob. 3P Ch. 4.7 - Prob. 4P Ch. 4.7 - Prob. 5P Ch. 4.7 - Prob. 6P Ch. 4.7 - Prob. 7P Ch. 4.7 - Prob. 8P Ch. 4.7 - Prob. 9P Ch. 4.7 - Prob. 10P Ch. 4.7 - Prob. 11P Ch. 4.7 - Prob. 12P Ch. 4.7 - Prob. 13P Ch. 4.7 - Prob. 14P Ch. 4.7 - Prob. 15P Ch. 4.7 - Prob. 16P Ch. 4.7 - Prob. 17P Ch. 4.7 - Prob. 18P Ch. 4.7 - Prob. 19P Ch. 4.7 - Prob. 20P Ch. 4.7 - Prob. 21P Ch. 4.7 - Prob. 22P Ch. 4.7 - Prob. 23P Ch. 4.7 - Prob. 24P Ch. 4.8 - Prob. 1P Ch. 4.8 - Prob. 2P Ch. 4.8 - Prob. 3P Ch. 4.8 - Prob. 4P Ch. 4.8 - Prob. 5P Ch. 4.8 - Prob. 6P Ch. 4.8 - Prob. 7P Ch. 4.8 - Prob. 8P Ch. 4.8 - Prob. 9P Ch. 4.8 - Prob. 10P Ch. 4.8 - Prob. 11P Ch. 4.8 - Prob. 12P Ch. 4.8 - Prob. 13P Ch. 4 - Prob. 1SYU Ch. 4 - Prob. 2SYU Ch. 4 - Prob. 3SYU Ch. 4 - Prob. 4SYU Ch. 4 - Prob. 5SYU Ch. 4 - Prob. 6SYU Ch. 4 - Prob. 7SYU Ch. 4 - Prob. 8SYU Ch. 4 - Prob. 9SYU Ch. 4 - Prob. 10SYU Ch. 4 - Prob. 11SYU Ch. 4 - Prob. 12SYU Ch. 4 - Prob. 13SYU Ch. 4 - Prob. 14SYU Ch. 4 - Prob. 15SYU Ch. 4 - Prob. 16SYU Ch. 4 - Prob. 17SYU Ch. 4 - Prob. 18SYU Ch. 4 - Prob. 19SYU Ch. 4 - Prob. 20SYU Ch. 4 - Prob. 21SYU Ch. 4 - Prob. 22SYU Ch. 4 - Prob. 23SYU Ch. 4 - Prob. 24SYU Ch. 4 - Prob. 25SYU Ch. 4 - Prob. 26SYU Ch. 4 - Prob. 27SYU Ch. 4 - Prob. 28SYU Ch. 4 - Prob. 29SYU Ch. 4 - Prob. 30SYU Ch. 4 - Prob. 31SYU Ch. 4 - Prob. 32SYU Ch. 4 - Prob. 33SYU Ch. 4 - Prob. 34SYU Ch. 4 - Prob. 35SYU Ch. 4 - Prob. 36SYU Ch. 4 - Prob. 37SYU Ch. 4 - Prob. 38SYU Ch. 4 - Prob. 39SYU Ch. 4 - Prob. 40SYU Ch. 4 - Prob. 41SYU Ch. 4 - Prob. 42SYU Ch. 4 - Prob. 43SYU Ch. 4 - Prob. 44SYU Ch. 4 - Prob. 45SYU Ch. 4 - Prob. 46SYU Ch. 4 - Prob. 47SYU Ch. 4 - Prob. 48SYU Ch. 4 - Prob. 49SYU Ch. 4 - Prob. 50SYU Ch. 4 - Prob. 51SYU Ch. 4 - Prob. 52SYU Ch. 4 - Prob. 53SYU Ch. 4 - Prob. 54SYU Ch. 4 - Prob. 55SYU Ch. 4 - Prob. 56SYU Ch. 4 - Prob. 57SYU Ch. 4 - Prob. 58SYU Ch. 4 - Prob. 59SYU Ch. 4 - Prob. 60SYU Ch. 4 - Prob. 61SYU Ch. 4 - Prob. 62SYU Ch. 4 - Prob. 63SYU Ch. 4 - Prob. 64SYU Ch. 4 - Prob. 65SYU Ch. 4 - Prob. 66SYU Ch. 4 - Prob. 67SYU Ch. 4 - Prob. 68SYU Ch. 4 - Prob. 69SYU Ch. 4 - Prob. 70SYU Ch. 4 - Prob. 71SYU Ch. 4 - Prob. 72SYU Ch. 4 - Prob. 73SYU Ch. 4 - Prob. 74SYU Ch. 4 - Prob. 75SYU Ch. 4 - Prob. 76SYU Ch. 4 - Prob. 77SYU Ch. 4 - Prob. 78SYU Ch. 4 - Prob. 79SYU Ch. 4 - Prob. 80SYU

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(a) To graph: f ( x ) = x 3 − a x for three different values of a.

Solution Summary: The author describes the graph of f(x)=x3-ax for three different values of a.

Concept explainers

Videos

(a)

To graph:

f(x)=x3−ax for three different values of a.

(b)

To describe:

The critical points of f and its appearance as a increases.

(c)

To find:

A formula for the x-coordinates of the critical points of f in terms of a.

Want to see the full answer?

Chapter 4 Solutions

(a) To graph: f ( x ) = x 3 − a x for three different values of a.

Solution Summary: The author describes the graph of f(x)=x3-ax for three different values of a.

Concept explainers

Videos

(a) To graph: f(x)=x3−ax for three different values of a.

(b) To describe: The critical points of f and its appearance as a increases.

(c) To find: A formula for the x-coordinates of the critical points of f in terms of a.

Want to see the full answer?

Chapter 4 Solutions

(a)

To graph:

f(x)=x3−ax for three different values of a.

(b)

To describe:

The critical points of f and its appearance as a increases.

(c)

To find:

A formula for the x-coordinates of the critical points of f in terms of a.