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1. (a) The image of code is given below
The image of the solution is given below. The value of sales in 2001 comes out to be 19.4 million
using interpolation technique. Here ‘a’ represents vector ’x’, ‘b’ represents vector ‘y’ and ‘c’
epresents value ‘xx’.
(b) To find the interpolating polynomial, we can use the MATLAB function p=ployfit(x,y,n)
Here
x=[1998, 1999, 2000, 2002, 2003, 2004]
y=[8, 12, 20, 18, 24, 26]
n=5
On calling the function ployfit(x,y,n), the solution comes out to be
1512293645 10*8178.110*54.410*54.410*2689.29374.5660567.0)(  xxxxxxp

(c)
2. (a) > x=[2,2.5,3,4,5,6.5,8]
x = 2.0000 2.5000 3.0000 4.0000 5.0000 6.5000 8.0000
y=[3,-1,3,-4,0,3,2]
y = 3 -1 3 -4 0 3 2
cubic_spline_natural(x,y,0,0,7)
0
16.0000
-15.0000
11.0000
-2.0000
-2.6667
0
i = 1 coef of s_1 are:
coef_x^3 = 20.21021432
coef_x^2 = -121.26128591
coef_x^1 = 229.47001824
coef_x^0 = -132.57660739
i = 2 coef of s_2 are:
coef_x^3 = -37.05107159
coef_x^2 = 308.19835841
coef_x^1 = -844.17909257
coef_x^0 = 762.13098495
i = 3 coef of s_3 are: ...