Explain for which values of a the function a* is increasing and for which values it is decreasing. Use the fact that, for a > 0, (а*) %3D (In a) a'. dx 'We are interested in when the derivative 2 is positive and when it is negative. The quantity a* is always positive. However, In a > 0 for a > 1 and In a < 0 for 0 < a < 1.Thus, the function a* is increasing for a > I and decreasing dx for a < 1. We are interested in when the derivative 2 is positive and when it is negative. The quantity a* is always positive. However, In a > 0 for a > e and In a < 0 for 0 < a < e. Thus, the function a* is increasing for a > e and decreasing for a < e. d(a") We are interested in when the derivative dx is positive and when it is negative. The quantity In a is always positive. However, a > O for a > 1 and a < 0 for 0 < a < 1. Thus, the function a" is increasing for a > I and decreasing for a < 1. d(a*) dx We are interested in when the derivative However, a > 0 for a > e and a < 0 for 0 < a < e. Thus, the function a* is increasing for a > e and decreasing for a < e. is positive and when it is negative. The quantity In a is always positive.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Explain for which values of a the function a* is increasing and for which values it is decreasing. Use the fact that, for a > 0,
(а*) %3D (In a) a'.
dx
'We are interested in when the derivative 2 is positive and when it is negative. The quantity a* is always positive.
However, In a > 0 for a > 1 and In a < 0 for 0 < a < 1.Thus, the function a* is increasing for a > I and decreasing
dx
for a < 1.
d(a")
We are interested in when the derivative
dx
is positive and when it is negative. The quantity a* is always positive.
However, In a > 0 for a > e and In a < 0 for 0 < a < e. Thus, the function a* is increasing for a > e and decreasing
for a < e.
d(a")
We are interested in when the derivative
dx
is positive and when it is negative. The quantity In a is always positive.
However, a > O for a > 1 and a < 0 for 0 < a < 1. Thus, the function a" is increasing for a > I and decreasing for
a < 1.
d(a")
dx
We are interested in when the derivative
However, a > O for a > e and a < 0 for 0 < a < e. Thus, the function a* is increasing for a > e and decreasing for
is positive and when it is negative. The quantity In a is always positive.
a < e.
Transcribed Image Text:Explain for which values of a the function a* is increasing and for which values it is decreasing. Use the fact that, for a > 0, (а*) %3D (In a) a'. dx 'We are interested in when the derivative 2 is positive and when it is negative. The quantity a* is always positive. However, In a > 0 for a > 1 and In a < 0 for 0 < a < 1.Thus, the function a* is increasing for a > I and decreasing dx for a < 1. d(a") We are interested in when the derivative dx is positive and when it is negative. The quantity a* is always positive. However, In a > 0 for a > e and In a < 0 for 0 < a < e. Thus, the function a* is increasing for a > e and decreasing for a < e. d(a") We are interested in when the derivative dx is positive and when it is negative. The quantity In a is always positive. However, a > O for a > 1 and a < 0 for 0 < a < 1. Thus, the function a" is increasing for a > I and decreasing for a < 1. d(a") dx We are interested in when the derivative However, a > O for a > e and a < 0 for 0 < a < e. Thus, the function a* is increasing for a > e and decreasing for is positive and when it is negative. The quantity In a is always positive. a < e.
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