27  Polynomials

\[ \newcommand{\dnorm}{\text{dnorm}} \newcommand{\pnorm}{\text{pnorm}} \newcommand{\recip}{\text{recip}} \]

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?

question id: terms-near-peak-1

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.

question id: terms-near-peak-2

27-reading.rmarkdown

No answers yet collected