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Using the approximation, explain why the second derivative test works

approximation=f(x0+delta x, y0+delta y)

delta x and delta y are small...

2. Relevant equations

f(x0+delta x,y0+delta y)

3. The attempt at a solution

ok so i know the first derivative of it is:

fx(x0+y0)*delta x+fy(x0+y0)*delta y

and second derivative is:

fxx(x0,y0)*delta x^2+fxy(x0,y0)*delta x*delta y+fyy(x0,y0)*delta y^2

it justs seems like since delta x and delta y are getting smaller,that everything will be going towards 0....so why does it work?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Using the approximation, explain why the second derivative test works.

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