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Proof using f(x1,y1)-f(x0,y0)=fx(x*,y*)(x1-x0)+fy(x*,y*)(y1-y0)

  1. Jun 17, 2012 #1
    1. The problem statement, all variables and given/known data[/prove f(x1,y1)-f(x0,y0)=fx(x*,y*)(x1-x0)+fy(x*,y*)(y1-y0)
    prove there exists a point (x*,y*)
    if fx and fy are all continuous on a circular region and contain A(x0,y0) and B(x1,y1)

    2. Relevant equations

    3. The attempt at a solution
    I'm thinking mean value theorem but honestly i have no idea how to do this.
    i dont even know how to properly apply the mean value theorem to this since there are two variables changing and the teacher said something about parametrization.
  2. jcsd
  3. Jun 17, 2012 #2

    Ray Vickson

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    Look at the univariate function [itex] g(t) = f(x_0 + t(x_1 - x_0), y_0 + t(y_1 - y_0))[/itex] on [itex] 0 \leq t \leq 1.[/itex]

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