Results 1 to 3 of 3

Math Help - Point on the graph minimize problem

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    9

    Point on the graph minimize problem

    Consider the function below.
    Find the point on the graph of function that is closest to the point (-3, 12).
    ( , 2)

    I know you have to use the distance formula and plug in your equation in for the y value. Differentiate simplify and set it equal to zero to minimize and solve for x. I keep getting stuck on the differentiation and solving for x.


    thanks in advance for any help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2005
    From
    Earth
    Posts
    1,599
    Here's a very useful hint. The distance formula has a square root in it, as you know, and thus is frustrating to differentiate. However take note of the fact that if you minimize D^2, you also minimize D. So try that out and if you're still stuck show your work and we'll find your error.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,663
    Thanks
    603
    Hello, thebacontalks2me!

    Consider the function: . f(x) \:=\:(x+9)^2 + 9

    Find the point on the graph of f(x) that is closest to the point A(\text{-}3, 12)
    Here's another useful procedure . . .

    Let the point be P(x,y), where y \:=\:(x+9)^2 + 9 \:=\:x^2 + 18x + 90


    Using Jameson's hint, let: . D \;=\;(x+3)^2 + (y - 12)^2

    . . Differentiate: . D' \;=\;2(x+3) + 2(y-12)\!\cdot\!y' \;=\;0


    Since y-12\:=\:x^2+18x+78, and y' \:=\:2x + 18

    . . we have: . 2(x + 3) + 2(x^2+18x+78)(2x+18) \;=\;0

    . . which simplifies to: . 2x^3 + 54x^2 + 481x + 1407 \:=\:0

    . . which factors: . (x+7)(2x^2 + 40x + 201) \;=\;0

    . . and has the real root: . x\:=\:\text{-}7

    Then: . y \:=\:(\text{-}7)^2 + 18(\text{-}7) + 90 \:=\:13


    Therefore, the nearest point is: . (\text{-}7,\,13)

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: November 1st 2010, 05:23 AM
  2. Replies: 9
    Last Post: July 20th 2010, 08:00 AM
  3. Replies: 1
    Last Post: April 27th 2009, 02:30 PM
  4. minimize problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 9th 2008, 10:38 PM
  5. Point on a CSC graph
    Posted in the Pre-Calculus Forum
    Replies: 7
    Last Post: October 5th 2007, 08:03 AM

Search Tags


/mathhelpforum @mathhelpforum