College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 3 - Polynomial and Rational Functions - Exercise Set 3.1: 61



Work Step by Step

See p.340: Strategy for Solving Problems lnvolving Maximizing or Minimizing Quadratic Functions 1. $\quad $Read the problem carefully and decide which quantity is to be maximized or minimized. 2. $\quad $Use the conditions of the problem to express the quantity as a function in one variable. 3. $\quad $Rewrite the function in the form $f(x)=ax^{2}+bx+c$. 4. $\quad $Calculate $-\displaystyle \frac{b}{2a}$. If $a>0, f$ has a minimum at $x=-\displaystyle \frac{b}{2a}$. This minimum value is $f$($-\displaystyle \frac{b}{2a}$). If $a<0, f$ has a maximum at $x=-2ab$. This maximum value is $f$($-\displaystyle \frac{b}{2a}$).. 5. $\quad $Answer the question posed in the problem. ---------------------------- 1. Product is to be maximized 2. Let x be one of the numbers. Then, the other number is 16-x Their product, $f(x)=x(16-x)$ is a quadratic function. 3.$\quad f(x)=16x-x^{2}$ $f(x)=-x^{2}+16x$ $4.\qquad a=-1, b=16, c=0$ $-\displaystyle \frac{b}{2a}=-\frac{16}{2(-1)}=8$ 5. The product is maximum when $x=8.$ The other number is $16-8=8.$ The maximum product is f(8)$=8(8)=64$
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