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Finding the minimum perimeter.

  1. Nov 12, 2012 #1
    1. The problem statement, all variables and given/known data

    I'm stuck on part b) of the question, but this includes the whole thing:

    A farmer wants to make a rectangular paddock with an area of 4000m^2. However, fencing costs are high and she wants the paddock to have a minimum perimeter.

    a) Show that the perimeter is given by the equation P = 2x + 8000/x

    b) Find the dimensions of the rectangle that will give the minimum perimeter, correct to 1 decimal place.


    3. The attempt at a solution

    a) A = 4000 = xy

    y = 4000/x

    P = 2x + 2y
    = 2x + 2(4000/x)
    = 2x + 8000/x

    Okay, so that was easy.

    b) I assume here I just find the first derivative of P (to find minima)

    dP/dx = 2 + 8000/x^2

    So; 8000/x^2 + 2 = 0

    Obviously this won't solve because I can't find x ( negative sq. root)... Where have I gone wrong exactly?
     
  2. jcsd
  3. Nov 12, 2012 #2
    The derivative wrt x of [itex]\frac{1}{x}[/itex] ie of x[itex]^{-1}[/itex] = -x[itex]^{-2}[/itex]= -[itex]\frac{1}{x^{2}}[/itex]
     
  4. Nov 12, 2012 #3
    So I should do P = 2x + 8000x^-1 instead... So x isn't on the bottom?

    Can you show me the solution?


    edit - Nvm, simple mistake with the derivative.
     
    Last edited: Nov 12, 2012
  5. Nov 13, 2012 #4
    Yes you just had a simple mistake with the derivative.

    Just replace the + with a - on the RHS of your derivative.
     
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