Results 1 to 4 of 4

Math Help - Hyperbola point

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    10

    Hyperbola point

    1) Find the point on the hyperbola xy=8 closest to (3,0).

    I honestly, have no idea what to do. I seriously do not remember discussing anything like this in class, nor having any previous problems in homework. If anyone can give me a start or walkthrough, that would be fantastic!

    hmm alright.

    Ive gotten too squareroot(x^2 - 6x + 9 +64/x^2)

    but am not sure how to get from there, to the minimum
    Last edited by ThePerfectHacker; March 28th 2009 at 12:56 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by karisrou View Post
    hmm alright.

    Ive gotten too squareroot(x^2 - 6x + 9 +64/x^2)

    but am not sure how to get from there, to the minimum
    Now differentiate (use the chain rule). Then equate the derivative to zero. After a bit of algebra you have

    x^4 - 3x^3 - 64 = 0.

    Now solve for x.

    I think you'll find that x = 4 gives the minimum value ....
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2009
    Posts
    10
    When you use the chain rule, wouldnt you have to put 2 times the radical below the derivative of the contents of the radical?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by karisrou View Post
    When you use the chain rule, wouldnt you have to put 2 times the radical below the derivative of the contents of the radical?
    Yes. Have you differentiated, equated to zero and done a bit of algebra ....? The you will get the quartic I posted.

    Note that if \frac{A}{B} = 0 then A = 0 \, ....
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: May 16th 2011, 04:57 AM
  2. Replies: 1
    Last Post: April 6th 2011, 06:44 AM
  3. Replies: 9
    Last Post: July 20th 2010, 08:00 AM
  4. Replies: 3
    Last Post: August 9th 2009, 11:53 AM
  5. Replies: 3
    Last Post: February 20th 2008, 10:17 AM

Search Tags


/mathhelpforum @mathhelpforum