anonymous
  • anonymous
help with optimization! (attached)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
anonymous
  • anonymous
okay i understand everything..... except how to find the minimum!
anonymous
  • anonymous
are you familiar with derivative?

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

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