1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Applied Optimization problem

  1. Nov 20, 2007 #1
    1. The problem statement, all variables and given/known data

    Find the area of the largest rectangle that can be inscribed in the region bounded by the graph of y = (4-x)/(2+x) and the coordinate aces in the first quadrant.

    I think my only problem with this one is taking the derivative,

    this is what i get y' = (-x^2 - 4x + 8)/(2+x)^2

    Critical numbers: [1-root(48)]/-2, but that doesn't seem to be giving me a maximum value, can someone take a second look this.
  2. jcsd
  3. Nov 20, 2007 #2
    If I'm not mistaken:

    A = xy, x = x, y = (4-x)/(2+x)

    A = x(4-x/2+x)
    = (4x - x^2 / 2 + x)

    Using Quotient Rule (feel free to use the product rule if you want to):
    dy/dx = ((2 + x)(4 -2x) - (4x - x^2)(1)) / (2 + x)^2

    =8 -4x +4x -2x^2 - 4x + x^2 / g^2
    dy/dx = 8 -x^2 -4x / 4 + 4x + x^2

    Graphing that, I can see 2 roots.
    (can't be bothered actually solving properly for them now though, :) )
    They are:
    -5.46410 & 1.464101

    Using 1.464101 leads to an area of about 1.0717
    Graphing the original function to be optimized, I see that this is correct.
  4. Nov 20, 2007 #3
    Okay, doing a poly long divide, I get the dy/dx as:
    -1 + 12/(x+2)(x+2) = 0
    x^2 + 4x - 8 = 0

    This is interestingly the numerator of the original function.

    Solving this with quadratic formula yields the same results.
  5. Nov 21, 2007 #4
    my error was in using the quadratic formula, i took -a instead of -b which is why i got a strange value.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook