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

1. mathcalculus

2. mathcalculus

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

3. completeidiot

are you familiar with derivative?

4. mathcalculus

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

5. mathcalculus

yes

6. mathcalculus

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. completeidiot

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. completeidiot

or x

9. mathcalculus

is there a way to do that without it?

10. completeidiot

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

11. mathcalculus

by hand

12. mathcalculus

no calculator

13. completeidiot

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

14. completeidiot

because the slope at the minimum point is zero

15. mathcalculus

can you show me?

16. mathcalculus

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

17. completeidiot

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

18. completeidiot

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

19. completeidiot

any questions?

20. Psymon

@completeidiot derivative is fine :3

21. mathcalculus

yeah 1/x?

22. completeidiot

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

23. completeidiot

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

24. mathcalculus

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

25. mathcalculus

then im lost

26. completeidiot

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. completeidiot

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

28. completeidiot

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

29. completeidiot

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

30. mathcalculus

i got it=]

31. mathcalculus

thanks!

32. completeidiot

no problem