Chapter 3.4, Problem 4E

Let $f(x)=3x{e}^x-e^{2x}$

1. Approximate $f(1.03)$ by the Hermite interpolating polynomial of degree at most 3 using $x_0=1$ and $x_1=\mathrm{1.05.}$ Compare the actual error to the error bound.
2. Repeat (a) with the Hermite interpolating polynomial of degree at most 5, using $x_0=1$, $x_1=1.05,$ and $x_2=1.07$.