Assume that the profit generated by a product is given by p (x) = 3√x where x is the number of units sold. If the profit keeps changing at a rate of $900 per month, then how fast are the sales changing when the number of units sold is 400?

Question

Cherish Cooke

Mathematics

22 July, 17:36

Assume that the profit generated by a product is given by p (x) = 3√x where x is the number of units sold. If the profit keeps changing at a rate of $900 per month, then how fast are the sales changing when the number of units sold is 400?

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Answers (1)

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Maya Blackburn · Answer 1

Check the explanation

Step-by-step explanation:

Using the chain rule: dp/dx = (dp/dt) / (dx/dt).

So, you can calculate dp/dx=2x^ (-1/2) = 2/√x.

by my original statement (rearranged a little) dx/dt (which is what you're looking for) is equal to (dp/dt) / (dp/dx), so subbing in x=1900 you get 1000√1900/2=21794.495 units/month increase in sales.