Question
Asked Oct 27, 2019
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Suppose total cost in dollars from the production of x printers is given by

C(x) = 0.0001x3 + 0.005x2 + 28x + 3000
 
(a) Find the average rate of change of total cost when production changes from 100 to 500 printers.


(b) Find the average rate of change of total cost when production changes from 500 to 700 printers.
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Expert Answer

Step 1

Suppose total cost in dollar from the production of x printers is given by

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

Find the average rate f change of total cost when production changes

  1. a) from 100 to 500 printers
  2. b) from 500 to 700 printer
Step 2

The average  rate of change of a function

help_outline

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y=f(x) from x ato bis defined by f(b)-f(a) b-a

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Step 3

Given

from 100 to 500...

help_outline

Image Transcriptionclose

f(b)-f(a) b-a C(x) 0.0001x + 0.005x2 +28x+3000 C(500) 0.0001(500)+0.005 (500) + 28 (500)+3000 12500+1250+14000+3000 30750 C(100) 0.0001(100) +0.005(100) +28(100)+3000 = 100+50+2800+3000 = 5950 Hence f(b)-f(a) У b-а f(500)-f(100) 500-100 30750-5950 500-100 24800 400 6200

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Tagged in

Math

Calculus