Math 132A Assignment 3
1. Find the first three terms of the Taylor series for
at the point x0 = (1, −1)T . Evaluate the sum of these first three terms at p = (0.1, 0.01). What is the approximate difference of this with the true value of f(x0 +p)?
2. Find the first three terms of the Taylor series for
at the point x0 = (3, 4)T .
3. Determine whether or not the following matrices are positive definite:
(a)
(b)
(c)
4. Determine all minimizers (if any) of the following functions:
(a)
(b)
(c)
5. Let f(x) = x2 +cos(x). Starting with the interval [1, 2], use the golden section method to locate an interval of width 0.1 that contains the minimizer x*.
(You should use a calculator for the calculations but organize your work in a table please.)