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## anonymous 2 years ago help with optimization! (attached)

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1. anonymous

2. anonymous

okay i understand everything..... except how to find the minimum!

3. anonymous

are you familiar with derivative?

4. anonymous

i know they got the equation. y=6x+(21000/x)

5. anonymous

yes

6. anonymous

then after i'm not sure how they got: Minimum occurs at 59.16 ft for the length (found on a graphing calc) width: 10500/59.16 = 177.5 ft Perimeter = 710 ft

7. anonymous

ok, well the method they got the minimum is just by using a graphing calculator with a max min function on it doing it manually would involve finding the first derivative of the equation and then setting it equal to zero and then solving for L

8. anonymous

or x

9. anonymous

is there a way to do that without it?

10. anonymous

without the graphing calculator? or without having to do it manually?

11. anonymous

by hand

12. anonymous

no calculator

13. anonymous

by hand would involve finding the first derivative of the equation and then setting it equal to zero and then solving for L

14. anonymous

because the slope at the minimum point is zero

15. anonymous

can you show me?

16. anonymous

im doing it wrong, even on calculator :/ I'm not getting it.

17. anonymous

$y = \frac{21000}{x} + 6x$ $y' = -\frac{21000}{x^2} +6$ $y' =0$ $0=-\frac{21000}{x^2} +6$ solve for x hopefully i didnt screw up the derivative

18. anonymous

$\frac{1}{x} = x^{-1}$

19. anonymous

any questions?

20. anonymous

@completeidiot derivative is fine :3

21. anonymous

yeah 1/x?

22. anonymous

im just pointing out the identity that allows you to use the "power" rule for derivatives

23. anonymous

$y= x^n$ $y' = nx^{n-1}$

24. anonymous

im not getting that. i got up to here: y=6-21000/x^2 then set it to 0

25. anonymous

then im lost

26. anonymous

1/x is not part of the problem you can ignore it if you want its just that the identity is sometimes not obvious to other people

27. anonymous

once you set it equal to zero 0=6-21000/x^2 just solve for x

28. anonymous

6= 21000/x^2 x^2= 21000/6 x = sqrt {21000/6}

29. anonymous

any other questions? sorry for any confusion i may have caused

30. anonymous

i got it=]

31. anonymous

thanks!

32. anonymous

no problem

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