# Calculus

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At the moment OHaganBooks is selling 1000 books per week and its sales are rising at a rate of 200 books per week. Also, it is now selling all its books for \$20 each, but the price is dropping at a rate of \$1 per week. I need to know at what rate OHaganBooks' revenue is rising or falling given these conditions. I would also like to see the company's revenue increase at a rate of \$5000 per week. At what rate would sales have to have been increasing to accomplish this?

Can somebody help me answer this and explain the steps to solve the problem?

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We tried to help you with this several days ago. What did you not understand?

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Michael I have a question for you about the simplifying and taking a derivative

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i am a different person and i still do not understand it
i get R'=3000-400X
but i don't understand wat to do with the 5000

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What is the basic formula for calculating revenue? Think about how a bookstore gets money if all its books are priced equally.

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R=p*q

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Right. Now how do you implicitly differentiate that?

Follow the product and chains rules.

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Follow the product and chain rules.**

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R'=p'(q)+p(q')

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All you have to do is read the problem and identify p', q, p, and q'. Plug them in to get your change in rate of revenue (R').

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ok i got
p=20
p'=-1
q=1000
q'=200
and when i plugged them in i got r'=3000
is that right?

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Yes, don't forget your dollar sign and labeling. (What does the \$3000 mean?)

For the second part, plug in R' = 5000 and fill in all your other variables except q'. Then, solve for q'.

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Ok \$3000 is the rate at that the revenue is rising.
Ok for the second answer i plugged it in and i got
30=q'

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The company's revenue increases at a rate of \$3000 per week. (You need the unit of time.)

Check your algebra for the second part.

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ok i redid it
so q'=300?

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Good work Michael, thanks.

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So sales must increase at a rate of 300 books per week.
Thank U So much!
im gonna work on the second half of the problem now.

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That's correct. Good job!

(Thanks, bobpursley.)

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