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!

Proof for Max/Min Problem

  1. Mar 8, 2006 #1
    We had to do a question in my Advanced Mathematics class, and the way that I did the problem was supposedly right. My teacher even did it that way. However, the answer was wrong, so my teacher showed us the correct way to do the problem.

    The dilemma I have is that BOTH ways should work, but they don't. :surprised Therefore, I am going to give both solutions to the problem, and I was wondering if you could tell me why the first one does not work.

    Question: The coordinates of points P and Q are (1,2) and (2,-3), respectively, and R is a point on the line x=-1. Find the coordinates of R so that PR + RQ is a minimum?

    Here is the graph/image I used for this problem:
    http://s62.yousendit.com/d.aspx?id=0LUTJESKXM0R33IOBSY2IH1Z3A

    MY SOLUTION:

    Equations: PR^2 = 2^2 + y^2
    QR^2 = 3^2 + (5 - y)^2

    PR^2 + QR^2 = minimum or m
    2^2 + y^2 + 3^2 + (5 -y)(5 - y) = minimum
    4 + y^2 + 9 + 25 - 10y + y^2 = minimum
    2y^2 - 10y + 38 = minimum

    y = -b/2a = 10/4 = 5/2

    Y-coordinate of R = 2 - 5/2 = -1/2

    Therefore, the coordinates of R are (-1, -1/2)

    CORRECT SOLUTION:

    Let m = minimum

    mP'R = [ (2 - y) / (-3 + 1) ] = [ (2 - y) / -2 ]

    mRQ = [ (y + 3) / (-1 -2) ] = [ (y + 3) / -3 ]

    Note: mP'R = mRQ
    [ (2 - y) / -2 ] = [ (y + 3) / -3 ]
    = -2y - 6 = 3y - 6
    = -5y = 0
    y = 0

    The coordinates of R are therefore (-1, 0).

    *So...I have presented both solutions, and I would highly appreciate your help. I am really interested in trying to understand this dilemma.

    Thanks
     
  2. jcsd
  3. Mar 9, 2006 #2

    NateTG

    User Avatar
    Science Advisor
    Homework Helper

    The maximum of the sum of the squares isn't necessarily the maximum of the sum.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Proof for Max/Min Problem
  1. Max/ min (Replies: 3)

  2. Min and max value of r (Replies: 17)

Loading...