Chapter 18, Problem 27P

The following is the built-in humps function that MATLAB uses to demonstrate some of its numerical capabilities:

$f\left(x\right)=\frac{1}{{\left(x-0.3\right)}^2+0.01}+\frac{1}{{\left(x-0.9\right)}^2+0.04}-6$

The humps function exhibits both fl at and steep regions over a relatively short x range. Generate values of this function at intervals of 0.1 over the range from $x=0$ to 1. Fit these data with a cubic spline and create a plot comparing the fit with the exact humps function.