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

f(x)= 1 + 1 6 (x 0.3)2 +0.01 (x 0.9)2 +0.04

The humps function exhibits both flat and steep regions over a relatively short x range. Here are some values that have been generated at intervals of 0.1 over the range from x = 0 to 1:

x00.10.20.30.40.5

f(x) 5.176 15.471 45.887 96.500 47.448 19.000

x 0.6 0.7 0.8 0.9 1 f (x) 11.692 12.382 17.846 21.703 16.000

Fit these data with a (a) cubic spline with not-a-knot end conditions and (b) piecewise cubic Hermite interpolation. In both cases, create a plot comparing the fit with the exact humps function.

183 The following is the built-in humps function that MATLAB uses to demonstrate some of its numerical capabilities: f(x )=(1-0.3.2 +0.01 + (x-097 +004-6 The humps function exhibits both flat and steep regions over a relatively short x range. Here are some values that have been generated at intervals of 0.1 over the range from x = 0 to 1 0 0.1 02 030405 fx) 5 176 15.471 45.887 96 500 47 448 19.000 x 06 07 0.8 09 f(x) 11692 12.382 17.846 21.703 16.000 Fit these data with a (a) cubic spline with not-a-knot end conditions and (b) piecewise cubic Hermite interpolation. In both cases, create a plot comparing the fit with the exact humps function