## brendakayyy Group Title help me with optimization for calculus one year ago one year ago

1. brendakayyy Group Title

a computer company determines its profit equation in millions of dollars given by p=x^3-48x^2+720x-1000 where x is the number of thousands of units of software sold

2. brendakayyy Group Title

and 0<x<40 optimize the manufactures profit

3. Goten77 Group Title

im thinking this is really ez.... but maybe im wrong.... since from 0-40 it looks like a line almost.... wouldnt (40,y) b the maximum?

4. Goten77 Group Title

or maybe im wrong

5. zepdrix Group Title

|dw:1355889094401:dw|It's a cubic function, so it's going to have this shape. As I've illustrated in the picture, it is possible that 40 might not be the maximum profit value. So we'll have to do some work to find out where that point is.

6. brendakayyy Group Title

do i differentiate the function and find the critical values?

7. zepdrix Group Title

$\large P(x)=x^3-48x^2+720x-1000$Yes very good. You'll want to find Critical Points, and since this is a CLOSED INTERVAL, also check the END POINTS! Then simply plug each value into the function, and see which gives you the largest output.

8. Goten77 Group Title

oh if thats how it looked then i graphed it wrong.. my bad

9. zepdrix Group Title

Hmm I better throw it into wolfram and make sure I'm not way off.. cause I was just doing that based off of memory :P

10. Goten77 Group Title

but anyways it be best to just find derivative.. and critical points.. then find values of those and the 0/40 and then u get ur answer

11. brendakayyy Group Title

would my critical values be x<12, 12<x<20, X>20?

12. Goten77 Group Title

ur critical valued would be points.....

13. Goten77 Group Title

|dw:1355889480030:dw|

14. zepdrix Group Title

You got the correct points, x=12, x=20. I'm not sure why you wrote them as intervals though :)

15. Goten77 Group Title

^ye

16. zepdrix Group Title

Now you want to plug your values into P(x) and compare, to find out which one gives you the largest value within this closed interval.$\large P(12),\quad P(20), \quad P(0), \quad P(40)$

17. brendakayyy Group Title

well cuz you base your values off the intervals according to my teacher

18. brendakayyy Group Title

what equation would i plug that into?

19. zepdrix Group Title

The original equation.

20. brendakayyy Group Title

ok got it

21. brendakayyy Group Title

whered you get the P(40) and P(0)

22. Goten77 Group Title

there apart of the domain.. so there possible maxs's mins

23. brendakayyy Group Title

oh thats what was meant by end points so if it were aclosed interval i would not take the end points into consideration right?

24. brendakayyy Group Title

what are the dimensions of the square based open top box that has a volume of 20 cubic inches and smallest surface area?

25. brendakayyy Group Title

can someone help me with this one ^

26. Zarkon Group Title

if you have a new question you should put it in a new thread