3-part Question: Rate of Change

Calculus
Tutor: None Selected Time limit: 1 Day

Suppose that for a company manufacturing calculators, the cost, and revenue equations are given by

C = 80000 + 20x

R = 400 - (x^2)/40

A) What is the rate of change in cost?

B) What is the rate of change in revenue?

C) What is the rate of change in profit?

Apr 2nd, 2015

Hey are you sure the question is complete? I think there are some parts missing. 

To find rates of change you need to take the derivative with respect to x. 

dC/dx = 20*dx = 20*dx 

dR/dx = - (1/20)xdx 


dP/dx = dR/dx - dC/dx = --0.05xdx-20dx

Apr 2nd, 2015

so sorry...I did forget an important piece...thank you...here is the rest of the information:


where the production output in one week is x calculators. If the production rate is increasing at a rate of 500 calculators when the production output is 6000 calculators, find each of the following: 

Apr 2nd, 2015

Cool, so

dC/dx = 20*dx = 20*500=10000

dR/dx = - (1/20)xdx = -0.05*500*6000= -150000


dP/dx = dR/dx - dC/dx = -150000-10000=-160000

P.S: Are you sure R = 400 - (x^2)/40? Is the equation correct?


Apr 2nd, 2015

yes i just checked the answers...everything is correct...thank you so much!

Apr 2nd, 2015

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