## pafoo 3 years ago A company has determined that when x items are sold daily, the profit P is given by P(x)=-0.002x^2+4.3x-120 What is the profit if 700 items are made? How many items should be made daily in order to maximize the companys profit? I know the first one is 1,910, but how do I maximize the company's profit?

1. RyanL.

This basically asks you to find the vertex of the equation

2. RyanL.

find the derivative and set it to zero

3. RyanL.

solve for x then

4. pafoo

What formula would I use?

5. RyanL.

I don't know any formulas but I do know how to find it using a derivative

6. pafoo

Ok, any advice on how I should proceed?

7. RyanL.

Find the derivative

8. pafoo

So if I get a derivative of 4.3-0.004x, what should I do then?

9. RyanL.

set it to zero and solve for x

10. RyanL.

4.3-0.004x=0

11. RyanL.

4.3-0.004x=0 -0.004x=-4.3 x=-4.3/-0.004 x=1075

12. RyanL.

1075 items

13. pafoo

i see, so the derivative is the key, awesome, thanks!

14. RyanL.

http://www.wolframalpha.com/input/?i=-0.002x%5E2%2B4.3x-120 if you graph it you can see the highest point right? That point is called the vertex and you can find it using the derivative

15. pafoo

Ah, ok I got you.