Calculus Concepts: An Informal Approach to the Mathematics of Change 5th Edition

Published by Brooks Cole
ISBN 10: 1-43904-957-2
ISBN 13: 978-1-43904-957-0

Chapter 1 - Ingredients of Change: Functions and Limits - 1.4 Activities - Page 42: 3

Answer

a. $2$ b. The profit is increasing by $2$ thousand dollars per hundred units sold. c. $-4.5$

Work Step by Step

$f(x)=2x-4.5=mx+c$ (a) Where m is slope and c is y-intercept $\Longrightarrow$ m=slope=2 (b) Change=f(x+$\delta x$)-f(x)=2(x+$\delta x$)-4.5-(2x-4.5) Change=2x+2$\delta x$-4.5-2x+4.5=2$\delta x$ $\Longrightarrow$ The profit is increasing by 2 thousand dollars per hundred units sold. (c) Putting x=0 in $f(x)=2x-4.5$ $f(0)=2(0)-4.5=-4.5$ $x=0$ $\Longrightarrow$ No units are sold When no units are sold the profit is -4.5 thousand
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