## mathcalculus Group Title help with optimization! (attached) 11 months ago 11 months ago

1. mathcalculus Group Title

2. mathcalculus Group Title

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

3. completeidiot Group Title

are you familiar with derivative?

4. mathcalculus Group Title

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

5. mathcalculus Group Title

yes

6. mathcalculus Group Title

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 Group Title

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 Group Title

or x

9. mathcalculus Group Title

is there a way to do that without it?

10. completeidiot Group Title

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

11. mathcalculus Group Title

by hand

12. mathcalculus Group Title

no calculator

13. completeidiot Group Title

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 Group Title

because the slope at the minimum point is zero

15. mathcalculus Group Title

can you show me?

16. mathcalculus Group Title

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

17. completeidiot Group Title

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

18. completeidiot Group Title

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

19. completeidiot Group Title

any questions?

20. Psymon Group Title

@completeidiot derivative is fine :3

21. mathcalculus Group Title

yeah 1/x?

22. completeidiot Group Title

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

23. completeidiot Group Title

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

24. mathcalculus Group Title

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

25. mathcalculus Group Title

then im lost

26. completeidiot Group Title

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 Group Title

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

28. completeidiot Group Title

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

29. completeidiot Group Title

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

30. mathcalculus Group Title

i got it=]

31. mathcalculus Group Title

thanks!

32. completeidiot Group Title

no problem