2. (Programming.) The upper portion of the noble beast in Figure 1 is plotted on the graph. Do the following and plot them on the same graph. (a) Use three clamped cubic splines to approximate the curves. (b) Use three Lagrange polynomials to approximate the curves.

(use for any programming language, preferably python or java)

2. (10 points) (Programming.) The upper portion of the noble beast in Figure 1 is plotted on the graph. Do the following and plot them on the same graph. (a) (7 points) Use three clamped cubic splines to approximate the curves. (b) (3 points) Use three Lagrange polynomials to approximate the curves. f(x) Slope Slope 3 Slope -4 8 7 6 Slope 1 5 4 Slope 3 2 Curve 1 -Curve 2 Curve 3 Slope 5 10 15 20 25 30 x Curve 1 Curve 2 Curve 3 i X; f (x;) f'(x) i X; f (x) f'(x) i X; f (x) f'(xi) 0 1 1.0 3.0 0 0.33 2 5 6 7 0 1 2 3 4 5 17 20 23 24 25 27 27.7 1 2 3 4.5 7.0 6.1 5.6 5.8 5.2 4.1 27.7 28 29 30 1 2 3 4 5 6 7 8 3.0 3.7 3.9 4.2 5.7 6.6 7.1 6.7 4.5 4.1 4.3 4.1 3.0 -1.5 8 6 -4.0 10 13 17 -0.67 2. (10 points) (Programming.) The upper portion of the noble beast in Figure 1 is plotted on the graph. Do the following and plot them on the same graph. (a) (7 points) Use three clamped cubic splines to approximate the curves. (b) (3 points) Use three Lagrange polynomials to approximate the curves. f(x) Slope Slope 3 Slope -4 8 7 6 Slope 1 5 4 Slope 3 2 Curve 1 -Curve 2 Curve 3 Slope 5 10 15 20 25 30 x Curve 1 Curve 2 Curve 3 i X; f (x;) f'(x) i X; f (x) f'(x) i X; f (x) f'(xi) 0 1 1.0 3.0 0 0.33 2 5 6 7 0 1 2 3 4 5 17 20 23 24 25 27 27.7 1 2 3 4.5 7.0 6.1 5.6 5.8 5.2 4.1 27.7 28 29 30 1 2 3 4 5 6 7 8 3.0 3.7 3.9 4.2 5.7 6.6 7.1 6.7 4.5 4.1 4.3 4.1 3.0 -1.5 8 6 -4.0 10 13 17 -0.67