   Chapter 9.3, Problem 39E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Total cost Suppose total cost in dollars from the production of x printers is given by C ( x ) = 0.0001 x 3 + 0.005 x 2 + 28 x + 3000 Find the average rate of change of total cost when production changes(a) from 100 to 300 printers.(b) from 300 to 600 printers.(c) Interpret the results from parts (a) and (b).

(a)

To determine

To calculate: The average rate of change of total cost when production changes from 100 to 300 printers. The total cost in dollars from the production of x printers is given by,

C(x)=0.0001x3+0.005x2+28x+3000

Explanation

Given Information:

The total cost in dollars from the production of x printers is given by,

C(x)=0.0001x3+0.005x2+28x+3000

Formula used:

The average rate of change of a function y=f(x) from x=a to x=b is defined by

Average rate of change=f(b)f(a)ba

Calculation:

Consider the provided function for total cost,

C(x)=0.0001x3+0.005x2+28x+3000

For x=100, substitute 100 for x in the given function,

C(100)=0.0001(100)3+0.005(100)2+28(100)+3000=0.0001(1000000)+0.005(10000)+2800+3000=100+50+5800=5950

For x=300, substitute 300 for x in the given function,

C(300)=0

(b)

To determine

To calculate: The average rate of change of total cost when production changes from 300 to 600 printers.

The total cost in dollars from the production of x printers is given by,

C(x)=0.0001x3+0.005x2+28x+3000

(c)

To determine

The interpretation from the average rate of change of total cost when production changes from 300 to 600 printers and when production changes from 100 to 300 printers. The total cost in dollars from the production of x printers is given by,

C(x)=0.0001x3+0.005x2+28x+3000

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