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Exercises 23.4 Homework

1.

(Theoretical) Complete the following formula for a clamped spline with boundary conditions \(S'(0) = -1\) and \(S'(3) = 6\text{:}\)

\begin{equation*} S(x)=\begin{cases} \dots & 0\le x\le 1,\\ 5 - 2x + x^3 & 1\le x\le 2,\\ \dots & 2\le x\le 3\end{cases} \end{equation*}
2.

Adapt Example 23.3.1 to find and plot the inflection points of the same cubic spline (these are the points where the second derivative is zero.)