Results 1 to 3 of 3

Math Help - directional derivative

  1. #1
    Junior Member
    Joined
    Feb 2013
    From
    Canada
    Posts
    44

    directional derivative

    The temperature at the point (x, y, z) in space is given by T(x, y, z) = x + yz. A fly is at the point (1, 2, 1). In what direction should he begin to fly to cool off as quickly as possible?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,651
    Thanks
    602

    Re: directional derivative

    Hey apatite.

    If the fly wants to cool off in the best way then the derivative with respect to the temperature must be minimal. What does this imply?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,652
    Thanks
    1597
    Awards
    1

    Re: directional derivative

    Quote Originally Posted by apatite View Post
    The temperature at the point (x, y, z) in space is given by T(x, y, z) = x + yz. A fly is at the point (1, 2, 1). In what direction should he begin to fly to cool off as quickly as possible?

    Actually  - \nabla f(a,b,c) points in the direction of most rapid decrease in the field determined by f.

    Recall that \nabla f = f_x i + f_y j + f_z k.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Lie Derivative (directional derivative proof)
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: November 28th 2012, 05:42 AM
  2. Directional derivative
    Posted in the Calculus Forum
    Replies: 6
    Last Post: July 20th 2011, 04:37 AM
  3. Directional derivative
    Posted in the Calculus Forum
    Replies: 6
    Last Post: May 17th 2009, 12:54 AM
  4. directional derivative
    Posted in the Calculus Forum
    Replies: 2
    Last Post: July 13th 2008, 02:53 PM
  5. Total Derivative vs. Directional Derivative
    Posted in the Advanced Math Topics Forum
    Replies: 5
    Last Post: May 30th 2008, 08:42 AM

Search Tags


/mathhelpforum @mathhelpforum