27  Polynomials

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Reading questions

Reading question 27.1 Imagine a quadratic approximation $\hat{f}(t)$ centered at the argmax $t^{\star }$ of a function $f(t)$. A generic formula is $$\hat{f}(t)\equiv a_0+a_1(t-t^{\star })+a_2(t-t^{\star }{)}^2$$ Is $\hat{f}(t)$ a polynomial? Which, if any, of the coefficients will be zero?

Reading question 27.2 Write down a complete quadratic approximation $\hat{g}(x,y)$ to a function $g(x,y)$, centering the approximation at an argmin, $(x^{\star },y^{\star })$. Use the standard notation for the coefficients, that is, $a_0,a_x,a_y,a_{xy}$ and so on.

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