Results 1 to 4 of 4

Math Help - finding f from gradient

  1. #1
    Junior Member
    Joined
    May 2012
    From
    Philadelphia
    Posts
    28

    finding f from gradient

    find f if grad f = 3xy i + x^3 j
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member Barioth's Avatar
    Joined
    Jan 2013
    From
    Canada
    Posts
    54
    Thanks
    16

    Re: finding f from gradient

    As you know grad f = \frac{d(f(x,y))}{dx}*i + \frac{d(f(x,y))}{dy}*j

    so I believe you could try integrating both part!

    Give that a try and let us know if it worked!

    Hope that helped, if not let me know!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,667
    Thanks
    1618
    Awards
    1

    Re: finding f from gradient

    Quote Originally Posted by Kvandesterren View Post
    find f if grad f = 3xy i + x^3 j

    I think that there is a typo in your post.

    Is it not, \nabla f(x,y) = 3x^2 yi + x^3 k~?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,707
    Thanks
    1470

    Re: finding f from gradient

    Quote Originally Posted by Kvandesterren View Post
    find f if grad f = 3xy i + x^3 j
    IF there exist a function f having that gradient, then we must have \frac{\partial f}{\partial x}= 3xy and \frac{\partial f}{\partial y}= x^3. If we differentiate the first a second time, but with respect to y, we have \frac{\partial^2 f}{\partial y\partial x}= 3x. If we differentiate the second a second time, but with respect to x, we have \frac{\partial^2 f}{\partial x\partial y}= 3x^2. As long as all derivatives are continuous, as they are here, the "mixed" second derivatives must be the same. Since this is not true, there is NO function, f, having 3xyi+ x^3j as its gradient.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding The Gradient Of A Matrix Equation
    Posted in the Calculus Forum
    Replies: 12
    Last Post: May 9th 2011, 07:57 PM
  2. Finding the gradient
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: December 14th 2009, 05:53 PM
  3. Finding Gradient
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 14th 2009, 01:54 AM
  4. Finding the gradient function.... lost
    Posted in the Calculus Forum
    Replies: 6
    Last Post: July 29th 2009, 06:01 AM
  5. [SOLVED] finding the gradient vector
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 27th 2009, 08:15 PM

Search Tags


/mathhelpforum @mathhelpforum