Results 1 to 3 of 3

Math Help - Proving a claim regarding differentiability

  1. #1
    Junior Member
    Joined
    Mar 2010
    Posts
    52

    Proving a claim regarding differentiability

    Let F(x,y,z) be a function which is defined in the point M_0(x_0,y_0,z_0) and around it and the following conditions are satisfied:

    1. F(x_0,y_0,z_0)=0
    2. F has continuous partial derivatives in M_0 and around it
    3. F'_z(x_0,y_0,z_0)=0
    4. gradF at (x_0,y_0,z_0) != 0
    5. It is known that there is a function f(x,y) so that F(x,y,f(x,y)) =0 in M_0 and around it

    Prove that f(x,y) is not differentiable in (x_0, y_0)
    Last edited by GIPC; January 19th 2011 at 07:21 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,453
    Thanks
    1868
    So, it is the "f" in (5) that you want to prove differentiable and not F?

    Do you recall the definition of "differentiable" for a function of two variables?

    f(x, y) is differentiable at (x_0, y_0) if and only if there exist a linear function L(x,y)= ax+ by and a function \epsilon(x,y) such that
    1) f(x, y)= F(x_0, y_0)+ a(x- x_0)+ b(y- y_0)+ \epsilon(x,y) and
    2) \lim_{(x,y)to (x_0,y_0)} \frac{\epsilon(x,y)}{\sqrt{(x-x_0)^2+ (y-y_0)^2}}= 0

    The demominator in (2) can be replaced with any reasonable measure of "distance" from (x_0, y_0)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2010
    Posts
    52
    I know the definition but I'm skeptical whether it helps here.

    I should probably use the chain rule somehow. Can't really point my finger how though.

    Help?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: November 25th 2010, 04:33 PM
  2. Proving differentiability
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 2nd 2010, 03:16 PM
  3. Proving differentiability
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 22nd 2009, 07:21 AM
  4. Testing a claim
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: April 29th 2008, 10:21 AM
  5. proving differentiability
    Posted in the Calculus Forum
    Replies: 7
    Last Post: August 4th 2007, 07:52 PM

Search Tags


/mathhelpforum @mathhelpforum