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mathcalculus

  • 2 years ago

help with optimization! (attached)

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  1. mathcalculus
    • 2 years ago
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  2. mathcalculus
    • 2 years ago
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    okay i understand everything..... except how to find the minimum!

  3. completeidiot
    • 2 years ago
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    are you familiar with derivative?

  4. mathcalculus
    • 2 years ago
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    i know they got the equation. y=6x+(21000/x)

  5. mathcalculus
    • 2 years ago
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    yes

  6. mathcalculus
    • 2 years ago
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    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
    • 2 years ago
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    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
    • 2 years ago
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    or x

  9. mathcalculus
    • 2 years ago
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    is there a way to do that without it?

  10. completeidiot
    • 2 years ago
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    without the graphing calculator? or without having to do it manually?

  11. mathcalculus
    • 2 years ago
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    by hand

  12. mathcalculus
    • 2 years ago
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    no calculator

  13. completeidiot
    • 2 years ago
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    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
    • 2 years ago
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    because the slope at the minimum point is zero

  15. mathcalculus
    • 2 years ago
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    can you show me?

  16. mathcalculus
    • 2 years ago
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    im doing it wrong, even on calculator :/ I'm not getting it.

  17. completeidiot
    • 2 years ago
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    \[y = \frac{21000}{x} + 6x\] \[y' = -\frac{21000}{x^2} +6\] \[y' =0\] \[0=-\frac{21000}{x^2} +6\] solve for x hopefully i didnt screw up the derivative

  18. completeidiot
    • 2 years ago
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    \[\frac{1}{x} = x^{-1}\]

  19. completeidiot
    • 2 years ago
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    any questions?

  20. Psymon
    • 2 years ago
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    @completeidiot derivative is fine :3

  21. mathcalculus
    • 2 years ago
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    yeah 1/x?

  22. completeidiot
    • 2 years ago
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    im just pointing out the identity that allows you to use the "power" rule for derivatives

  23. completeidiot
    • 2 years ago
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    \[y= x^n\] \[y' = nx^{n-1}\]

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

  25. mathcalculus
    • 2 years ago
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    then im lost

  26. completeidiot
    • 2 years ago
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    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
    • 2 years ago
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    once you set it equal to zero 0=6-21000/x^2 just solve for x

  28. completeidiot
    • 2 years ago
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    6= 21000/x^2 x^2= 21000/6 x = sqrt {21000/6}

  29. completeidiot
    • 2 years ago
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    any other questions? sorry for any confusion i may have caused

  30. mathcalculus
    • 2 years ago
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    i got it=]

  31. mathcalculus
    • 2 years ago
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    thanks!

  32. completeidiot
    • 2 years ago
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    no problem

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