Results 1 to 6 of 6

Math Help - Points on horizontal tangent plane?

  1. #1
    Member nautica17's Avatar
    Joined
    Aug 2009
    Posts
    121

    Points on horizontal tangent plane?

    This is a question from my calculus 3 class.

    "Find all points on the surface at which the tangent plane is horizontal."
    z = x^2 - xy + y^2 - 2x + 4y

    Okay, so I'm not sure where to begin. I know that the partial derivatives z_x and z_y are both zero. And so I've thought of making a tangent equation but I got stuck.

    Tangent plane = (z - z0) ?

    I'm not sure if I have to solve for x and y in the given equation, or really what I have to do in general.

    Can anyone give me a push in the right direction? Maybe I'm over-thinking this problem.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Dec 2009
    Posts
    226
    Like you said, \dfrac{\delta z}{\delta x} = 0 and \dfrac{\delta z}{\delta y} = 0, which is a system of equations. Solutions to the system of equations are the points on the surface at which the tangent plane is horizontal.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member nautica17's Avatar
    Joined
    Aug 2009
    Posts
    121
    This might be a silly question but how do I go about solving this? I know how to solve systems of equations, but all I see is dz/dx = 0 and dz/dy = 0. What am I not seeing?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Dec 2009
    Posts
    226
    First, find \dfrac{\delta z}{\delta x} given z = x^2 - xy + y^2 - 2x + 4y like so:

    \dfrac{\delta z}{\delta x} = 2x - y - 2

    Then, find \dfrac{\delta z}{\delta y} like so:

    \dfrac{\delta z}{\delta y} = 2y - x + 4

    Now, we know:

    2x - y - 2 = 0
    -x + 2y + 4 = 0

    I assume you can solve the systems of equation from here. If not, then feel free to post again.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Dec 2009
    Posts
    226
    If a moderator would delete this double post, then I would be much obliged. :P
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member nautica17's Avatar
    Joined
    Aug 2009
    Posts
    121
    Oooooh okay I see. Thanks!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Horizontal tangent points
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 21st 2011, 03:00 PM
  2. Horizontal Tangent Plane
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 11th 2009, 03:05 AM
  3. find horizontal tangent plane
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 12th 2009, 03:10 PM
  4. Replies: 2
    Last Post: May 9th 2009, 10:35 AM
  5. Replies: 3
    Last Post: March 28th 2009, 08:18 PM

Search Tags


/mathhelpforum @mathhelpforum