Results 1 to 2 of 2

Math Help - Optimization Problem

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    62

    Optimization Problem

    Problem: Which point on the parabola y = x^2 is nearest to (4, 0)? Find the coordinates to two decimals. (Hint: Minimize the square of the distance to avoid square roots.)


    What I've Done:
    I drew a picture to try and help me solve it, and tried to make a triangle between the curve x^2 and
    the point (4 , 0). I just don't really know how to get any equations for the problem.

    Help? I'd really appreciate it!
    Last edited by lysserloo; November 8th 2009 at 10:31 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by lysserloo View Post
    Problem: Which point on the parabola y = x^2 is nearest to (4, 0)? Find the coordinates to two decimals. (Hint: Minimize the square of the distance to avoid square roots.)


    What I've Done:
    I drew a picture to try and help me solve it, and tried to make a triangle between the curve x^2 and
    the point (4 , 0). I just don't really know how to get any equations for the problem.

    Help? I'd really appreciate it!
    A general point on the curve y=x^2 is (x,x^2), and the square distance from this point to (4,0) is:

    D^2=(x-4)^2+(x^4)

    Now we want to find the x that minimises D^2 and we do this by solving (D^2)'=0

    Which leaves you with the equation:

    2x^3+x-4=0

    which has one positive root and no negative roots (Descartes rule of signs tell us this), and this positive root is of necessity a minimum for D^2.

    You are expected to find this root numerically.

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Optimization Problem.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 5th 2010, 02:44 AM
  2. Optimization Problem
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: March 27th 2010, 02:35 PM
  3. Optimization Problem 2
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 8th 2009, 09:59 AM
  4. Optimization Problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 16th 2008, 01:21 PM
  5. Optimization Problem
    Posted in the Calculus Forum
    Replies: 5
    Last Post: November 19th 2007, 03:04 AM

Search Tags


/mathhelpforum @mathhelpforum