Results 1 to 7 of 7

Math Help - Calculus question

  1. #1
    Newbie
    Joined
    Jul 2007
    Posts
    12

    Calculus question

    I was wondering if I did the following problem right:

    Write the equation of the plane tangent to the given surface at the given point P.

    xyz+ 2x^3 - y^2 + z^2 = 10; P(2, -1, -1)

    So what I did was find the gradient of the above and got:

    <yz + 4x, xz - 2y, xy - 2z>

    Substituting P in I got, a normal vector of <9, 0, 0>

    This led to a plane equation of:
    9(x - 2) = 0
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by meebo0129 View Post
    I was wondering if I did the following problem right:

    Write the equation of the plane tangent to the given surface at the given point P.

    xyz+ 2x^3 - y^2 + z^2 = 10; P(2, -1, -1)

    So what I did was find the gradient of the above and got:

    <yz + 4x, xz - 2y, xy - 2z>

    Substituting P in I got, a normal vector of <9, 0, 0>

    This led to a plane equation of:
    9(x - 2) = 0
    Try again, you got the gradient all wrong.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2007
    Posts
    12
    Okay...here's my second attempt:

    (x-2)(yz-2x) + (y+1)(xz-2y) + (z+1)(xy-2z) = 0

    (x-2)(1-4)+(y+1)(-2+2)+(z+1)(-2+2)=0

    Then, I simplified this to:
    -3(x-2)=0
    x-2 = 0

    x = 2 <- equation of plane

    Would this be correct?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,962
    Thanks
    1784
    Awards
    1
    You have been told: "the gradient is all wrong."
    \begin{array}{rcl}<br />
 \nabla F & = & \left\langle {\partial _x F,\partial _y F,\partial _z F} \right\rangle  \\ <br />
  & = & \left\langle {yz + 4x ,xz - 2y,xy + 2z} \right\rangle  \\ <br />
 \end{array}<br />
    Last edited by Plato; August 3rd 2007 at 10:27 AM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jul 2007
    Posts
    12
    Oh, you know what? I accidentally wrote 2x^3 for the second term instead of 2x^2, which is what it was supposed to be. If this is the case, then is my original response correct?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,962
    Thanks
    1784
    Awards
    1
    O.K. I have corrected the above.
    But note the your "z" component should be with a +.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    May 2007
    Posts
    237
    Quote Originally Posted by meebo0129 View Post
    Write the equation of the plane tangent to the given surface at the given point P.

    xyz+ 2x^3 - y^2 + z^2 = 10; P(2, -1, -1)
    I was wondering if P(2,-1,-1) is on the given surface.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Question from Calculus Mid
    Posted in the Calculus Forum
    Replies: 7
    Last Post: November 20th 2011, 08:03 PM
  2. Replies: 1
    Last Post: February 11th 2010, 08:09 AM
  3. Calculus AP Question
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 14th 2007, 04:46 PM
  4. Calculus Question
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 19th 2006, 02:24 AM
  5. Calculus Question
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 18th 2006, 04:32 PM

Search Tags


/mathhelpforum @mathhelpforum