Practice for quiz 3

Here are a few more practice problems for our next quiz this Friday.

Problems

1. We’d like to generate a rational approximation to \(\sqrt{8}\). To do so, let \(f(x) = x^2 - 8\) and let \(x_0=1\). Then,

   1. Write down the corresponding Newton’s method iteration function for \(f\).
   2. Compute two Newton steps from \(x_0=1\).

2. Figure 1 shows the graph of \(f(x) = x\,e^{-x^2}\). Find the exact locations of any inflection points that you see.

3. I’ve got 1000 meters of fence to build a corral. The corral will be partitioned into three pieces as shown in Figure 2. What is the maximal total area that I can enclose?

Figures

Figure 1: The graph of \(f(x) = xe^{-x^2}\).

Figure 2: A corral partitioned into three pieces.