Let f a function of two variables at a point(a,b) The first degree Taylor polyno

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Let f a function of two variables at a point(a,b)
The first degree Taylor polynomial of f at (a,b) is L(x,y)=f(a,b)+fx(a,b)(x-a)+fy(a,b)(y-b)

If f has continious second-order partial derivatives at (a,b)then the second-degree Taylor polynomial of f at(a,b) is
Q(x,y)=f(a,b)+fx(a,b)(x-a)+ fy(a,b)(y-b) +1/2 fxx(a,b)(x-a)2+fxy(a,b)(x-a)(y-b)+1/2fyy(a,b)(y-b)2andthe approximation f(x,y)˜Q(x,y) is called tha quadraticapproximation to f at(a,b).
Verify that Q has the same firs- and second order partialderivatives as f at (a,b).
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