Results 1 to 4 of 4

Math Help - derivative

  1. #1
    Newbie
    Joined
    May 2009
    Posts
    3

    derivative

    find all the points on the graph x^4+y^4+2=4xy^3
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by eayettey View Post
    find all the points on the graph x^4+y^4+2=4xy^3
    Your question as asked does not make sense...

    Do you mean graph it?

    Since the title mentioned a derivative we can use implicit differentation to find it.

    4x^3+4y^3\frac{dy}{dx}=4y^3+12xy^2\frac{dy}{dx}

    From here you can solve for \frac{dy}{dx}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2009
    Posts
    11
    i have this same problem and it says "Find all points on the graph x^4+y^2+2=4xy^3 at which the tangent line is horizontal" He forgot to add "the tangent line is horizontal". This same problem is getting me too
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by gtgamer140@yahoo.com View Post
    i have this same problem and it says "Find all points on the graph x^4+y^2+2=4xy^3 at which the tangent line is horizontal" He forgot to add "the tangent line is horizontal". This same problem is getting me too
    Ahhhh so now we can finish

    So we know at the horizontal tangents that the derivative is zero

    \frac{dy}{dx}=0

    Now using the equation from above we get

    4x^3+4y^3\frac{dy}{dx}=4y^3+12xy^2\frac{dy}{dx}

    4x^3=4y^3 \iff y=x

    Now if we plug this back into the original equation we get

    x^4+y^4+2=4xy^3 setting y=x we get

    x^4+x^4+2=4x^4 \iff 0=2x^4-2 \iff 0=2(x^4-1)

    0=2(x^2-1)(x^2+1) \iff 0 =2(x-1)(x+1)(x^2+1)

    so it happens when x=\pm 1

    So when x=1 we get

    1+y^4+2=4y^3 \iff y^4-4y^3+3=0

    Now by the rational roots theorem we know the only possible rational roots are \pm1, \pm 3

    If you check on y=1 works so (1,1) is a horizontal tangent

    I will leave the other cases for you to check.

    Note there may be other Real roots
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. contuous weak derivative $\Rightarrow$ classic derivative ?
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: April 22nd 2011, 02:37 AM
  2. Replies: 0
    Last Post: January 24th 2011, 11:40 AM
  3. [SOLVED] Definition of Derivative/Alt. form of the derivative
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 23rd 2010, 06:33 AM
  4. Derivative Increasing ==> Derivative Continuous
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: February 23rd 2010, 10:58 AM
  5. Replies: 2
    Last Post: November 6th 2009, 02:51 PM

Search Tags


/mathhelpforum @mathhelpforum