Question: Explain the following, emphasizing the role of approximation. You need to only answer one of them.

1. Explain how to solve \(f(x, y)=a\) and \(g(x, y)=b\) simultaneously (Newton's method).
2. Explain how the multivariable chain rule follows from linearization considerations in the composition of \(f(g(x, y), h(x, y)) .\) Do this by considering the linearizations of \(g\) and \(h\) at \((a, b)\) and of \(f\) at the appropriate point.
3. Explain how the second derivative test follows from the second order Taylor polynomial.

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