A function ( ) is going to be approximated using an interpolation function for 0 ≤  ≤ 3. The second, ( ), and fourth, ( ), derivatives of the function are plotted in Figure 5.24. (a) How many data...

A function
() is going to be approximated using an interpolation function for 0 ≤
 ≤ 3. The second,
(), and fourth,
(), derivatives of the function are plotted in Figure 5.24.

(a) How many data points for piecewise linear interpolation are needed to guarantee the error is less than 10⁻⁸?

(b) How many data points for a clamped cubic spline are needed to guarantee the error is less than 10⁻⁸?