Explanation ( x ) = f ( x − a 1 ) f ( x − a 2 ) = e − A 2 ( x − a 2 ) = e − A 2 ( x − a 1 ) 2 + ( x − a 2 ) 2 Since e − 4 2 y is a decreasing function of y , It attains its maximum value where y is minimum Therefore, we must find the minimum value of y = (... To determine b) Show that for any n , ϕ attains its maximum value at x = 1 n ( a 1 + a 2 + ..... a n ) role f ( x )

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

4th Edition

ISBN: 9781319312886

Author: Rogawski, Jon, Adams, Colin, FRANZOSA, Robert

Publisher: W. H. Freeman

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Question

Chapter 4, Problem 89CRE

To determine

a)

Assume $n = 2$ and prove that $ϕ (x)$ attains its maximum value at the average $x = \frac{1}{2} (a_{1} + a_{2})$ calculate $ϕ (x)$ using logarithm differentiation

To determine

b)

Show that for any

$n, ϕ$ attains its maximum value at

$x = \frac{1}{n} (a_{1} + a_{2} + ..... a_{n})$ role $f (x)$

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Chapter 4, Problem 88CRE

Chapter 5.1, Problem 1PQ

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Chapter 4 Solutions

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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Knowledge Booster

a) Assume n = 2 and prove that ϕ ( x ) attains its maximum value at the average x = 1 2 ( a 1 + a 2 ) calculate ϕ ( x ) using logarithm differentiation

a) Assume n=2 and prove that ϕ(x) attains its maximum value at the average x=12(a1+a2) calculate ϕ(x) using logarithm differentiation

b) Show that for any n,ϕ attains its maximum value at x=1n(a1+a2+.....an) role f(x)

Want to see the full answer?

Chapter 4 Solutions

a)

Assume $n = 2$ and prove that $ϕ (x)$ attains its maximum value at the average $x = \frac{1}{2} (a_{1} + a_{2})$ calculate $ϕ (x)$ using logarithm differentiation

b)

Show that for any

$n, ϕ$ attains its maximum value at

$x = \frac{1}{n} (a_{1} + a_{2} + ..... a_{n})$ role $f (x)$