(adsbygoogle = window.adsbygoogle || []).push({}); 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)= x^{2}+y^{2}; L(x,y)=2y-2x-2

Formula for local linear approximation is

f(x,y)+f_{x}(x,y)+f_{y}(x,y)=L(x,y)

So plugging in my known values

x0^{2}+y0^{2}+2x0(x-x0)+2y0(y-y0)=x^{2}+y^{2}

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

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# Homework Help: Linear approximation

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