Results 1 to 6 of 6

Math Help - max/min

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

    max/min

    there is one critical point for z=yx^5 + xy^5 + xy. Find it.

    Is the critical point (0,0)?
    Last edited by apatite; March 8th 2013 at 01:13 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Oct 2012
    From
    Ireland
    Posts
    591
    Thanks
    159

    Re: max/min

    There is a critical point when dz/dy and when dz/dx are equal to zero
    dz/dx= 5yx5y-1+ y5+ y
    This is zero at (0,0)

    dz/dx= x5ylnx5+ 5xy4+ x
    This is not defined at (0,0) because ln0 is not defined.

    I do not know how to find the critical point but (0,0) is not it
    Last edited by Shakarri; March 8th 2013 at 11:28 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2013
    From
    Canada
    Posts
    44

    Re: max/min

    .....
    Last edited by apatite; March 8th 2013 at 01:14 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Feb 2013
    From
    Canada
    Posts
    44

    Re: max/min

    Quote Originally Posted by Shakarri View Post
    There is a critical point when dz/dy and when dz/dx are equal to zero
    dz/dx= 5yx5y-1+ y5+ y
    This is zero at (0,0)

    dz/dx= x5ylnx5+ 5xy4+ x
    This is not defined at (0,0) because ln0 is not defined.

    I do not know how to find the critical point but (0,0) is not it
    Sorry, its yx^5 not x^5y
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,707
    Thanks
    1470

    Re: max/min

    Okay, so what are \partial z/\partial x and \partial z/\partial y? Where are they both equal to 0?

    By the way, in response to Shakarri's comment, a critical point is where the derivative is 0 or where the derivative does not exist.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Feb 2013
    From
    Canada
    Posts
    44

    Re: max/min

    Quote Originally Posted by HallsofIvy View Post
    Okay, so what are \partial z/\partial x and \partial z/\partial y? Where are they both equal to 0?

    By the way, in response to Shakarri's comment, a critical point is where the derivative is 0 or where the derivative does not exist.
    fx(x,y)= 5yx^4+y^%+y
    fy(x,y)= x^5+5xy^4+x

    so x=0 and y=0?
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum