Using python. You may import functions from the math, copy,matplotlib.plot and numpy.You may NOT use numpy.linalg.lstsq(). You may use fsolve() and quad() from scipy, but nothing else.

b) Write a program that demonstrates the Least Squares Curve Fitting method. You must write and call at least the following 3 functions: def Cubicspline (x, y, slopel=0, slope2=0): #calculates and returns a matrix containing the coefficients of the cubic splines. Slopel and slope2 are the slopes at the first and last points. def PlotCubicSpline (x, y, slopel, slope2, showpoints=True, npoints=500) : #calls CubicSpline, generates data points and plots the cubic spline curve. If showpoints is True, also put the original data on the same plot. def main() : A main program that uses the data and slopes given below to: 1. Call CubicSpline to generate and print the coefficients. 2. Call PlotCubicSpline to display a plot of the cubic spline. X=np.array([1.5, 3, 4.5, 6, 7.5, 9]) y=np.array([3.5, 1.5, -2, 6.9, 8.2 ,1.5]) slope1=2 slope2=-4 b) Write a program that demonstrates the Least Squares Curve Fitting method. You must write and call at least the following 3 functions: def Cubicspline (x, y, slopel=0, slope2=0): #calculates and returns a matrix containing the coefficients of the cubic splines. Slopel and slope2 are the slopes at the first and last points. def PlotCubicSpline (x, y, slopel, slope2, showpoints=True, npoints=500) : #calls CubicSpline, generates data points and plots the cubic spline curve. If showpoints is True, also put the original data on the same plot. def main() : A main program that uses the data and slopes given below to: 1. Call CubicSpline to generate and print the coefficients. 2. Call PlotCubicSpline to display a plot of the cubic spline. X=np.array([1.5, 3, 4.5, 6, 7.5, 9]) y=np.array([3.5, 1.5, -2, 6.9, 8.2 ,1.5]) slope1=2 slope2=-4