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Linear approximation

  1. Oct 10, 2012 #1
    1. The problem statement, all variables and given/known data
    Hey guys I'm having a hard time understanding how the book obtained the solution.

    Here is the question

    A function f is given along with a local linear approximation of L to f at a point P. Use the information given to determine point P.

    f(x,y)= x2+y2; L(x,y)=2y-2x-2

    Formula for local linear approximation is

    f(x,y)+fx(x,y)+fy(x,y)=L(x,y)

    So plugging in my known values

    x02+y02+2x0(x-x0)+2y0(y-y0)=x2+y2

    I was able to get up to here, and then when I looked at the solution in the book, it simply said x0=-1 y0 =1 and it isn't obvious to me why.

    Any help is appreciated


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 10, 2012 #2

    LCKurtz

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    That isn't correct.

    That is the correct linear approximation near ##(x_0,y_0)##. Buy why do you set it equal to your original ##f(x,y)##? The linear approximation is an approximation to ##f(x,y)## but not equal to it unless ##f(x,y)## is linear itself. But you are given the formula for the linear approximation, which I have highlighted in red. Set it equal to that and see if you can see how they got that answer.
     
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