mathcalculus
help with optimization! (attached)
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mathcalculus
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mathcalculus
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okay i understand everything..... except how to find the minimum!
completeidiot
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are you familiar with derivative?
mathcalculus
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i know they got the equation.
y=6x+(21000/x)
mathcalculus
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yes
mathcalculus
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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
completeidiot
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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
completeidiot
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or x
mathcalculus
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is there a way to do that without it?
completeidiot
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without the graphing calculator?
or without having to do it manually?
mathcalculus
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by hand
mathcalculus
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no calculator
completeidiot
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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
completeidiot
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because the slope at the minimum point is zero
mathcalculus
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can you show me?
mathcalculus
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im doing it wrong, even on calculator :/ I'm not getting it.
completeidiot
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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
completeidiot
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\[\frac{1}{x} = x^{-1}\]
completeidiot
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any questions?
Psymon
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@completeidiot derivative is fine :3
mathcalculus
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yeah 1/x?
completeidiot
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im just pointing out the identity that allows you to use the "power" rule for derivatives
completeidiot
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\[y= x^n\]
\[y' = nx^{n-1}\]
mathcalculus
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im not getting that. i got up to here:
y=6-21000/x^2 then set it to 0
mathcalculus
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then im lost
completeidiot
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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
completeidiot
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once you set it equal to zero
0=6-21000/x^2
just solve for x
completeidiot
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6= 21000/x^2
x^2= 21000/6
x = sqrt {21000/6}
completeidiot
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any other questions?
sorry for any confusion i may have caused
mathcalculus
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i got it=]
mathcalculus
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thanks!
completeidiot
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no problem