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# At that moment, what is the rate of change of profit, dp/dt?

For Luce Landscaping, the total revenue and the total cost for yard maintenance of x homes are given by R(x)=1000x-x^2 and C(x)=3000+20x. Suppose that Luce is adding 10 homes per day at the moment when the 400th customer is signed. At that moment, what is the rate of change of profit, dp/dt?

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- AshLv 72 months agoFavorite Answer
Profit P(x) = R(x) - C(x)

P(x) = 1000x - x² - (3000+20x)

P(x) = 1000x - x² - 3000 - 20x

P(x) = - x² + 980x - 3000

Given dx/dt = 10, for x = 400

Change in profit, dP/dt = -2x dx/dt + 980

dP/dt = -2(400)(10) + 980

dP/dt = -7,020

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