a) Plot the data points with a circle marker (Python).b) Plot the unique interpolating polynomial of maximum order (passes exactlythrough each point) and print the equation of the polynomial (in the form y = anxn+ an-1xn-1 + ... + a1x + a0) to the screen using python. Don't use polyfit &polyval for this problem; use the given data points to construct the matrix formfor the unknowns and solve it using python to find the polynomial coefficients.c) compute the linear spline equation for each segment by hand. Include thedomain. Plot the individual linear spline for every interval using pythond) Plot the "not-a-knot" cubic spline (python).Make sure b,c & d are shown in different colors. Include a legend on the graph.Make observations from the final plot with all the curves.I-4 -2 0 1 2 3y -10 3 8 25 52 36

Introduction polynomial interpolation: A technique for guessing values between known data points is polynomial interpolation. When there is a gap in graphical data but data is accessible on each side of the gap or at a few specified places inside the gap, interpolation can be used to estimate the values inside the gap.Source Code: close all;clear all;x=[-4 -2 0 1 2 3];y=[-10 3 8 25 52 36]; %Answer part(a)plot(x,y,'o');hold on; %Answer part(b)% Since there are 6 data points a 5th degree polynomial will uniquely fit it% Let it be of the form Y=C1*X^5+C2*X^4+C3*X^3+C4*X^2+C5*X+C6% First form the coefficient matrixfor i=1:6 for j=1:6 A(i,j)=x(i)^(6-j); endendC=A\y'; %Use of backslash functionY=@(C,X)C(1)*X^5+C(2)*X^4+C(3)*X^3+C(4)*X^2+C(5)*X+C(6);%use of function handleezplot(@(X)Y(C,X),[-4,3])h=ezplot(@(X)Y(C,X),[-4,3]);set(h,'Color','k')hold on %Answer part(c)%Equation of the linear spline is given as %y=((x(i)-x)/(x(i)-x(i-1)))*y(i-1)+((x-x(i-1))/(x(i)-x(i-1)))*y(i)%for the domain [x(i-1),x(i)]Xc=-4:0.01:3;for i=1:length(Xc) if Xc(i)>=x(1) && Xc(i)<=x(2) m=2;n=1; Yc(i)=((x(m)-Xc(i))/(x(m)-x(n)))*y(n)+((Xc(i)-x(n))/(x(m)-x(n)))*y(m); end if Xc(i)>=x(2) && Xc(i)<=x(3) m=3;n=2; Yc(i)=((x(m)-Xc(i))/(x(m)-x(n)))*y(n)+((Xc(i)-x(n))/(x(m)-x(n)))*y(m); end if Xc(i)>=x(3) && Xc(i)<=x(4) m=4;n=3; Yc(i)=((x(m)-Xc(i))/(x(m)-x(n)))*y(n)+((Xc(i)-x(n))/(x(m)-x(n)))*y(m); end if Xc(i)>=x(4) && Xc(i)<=x(5) m=5;n=4; Yc(i)=((x(m)-Xc(i))/(x(m)-x(n)))*y(n)+((Xc(i)-x(n))/(x(m)-x(n)))*y(m); end if Xc(i)>=x(5) && Xc(i)<=x(6) m=6;n=5; Yc(i)=((x(m)-Xc(i))/(x(m)-x(n)))*y(n)+((Xc(i)-x(n))/(x(m)-x(n)))*y(m); end endplot(Xc,Yc,'r'); %Answer part(d)%Select Tools---->Basic Fitting---->SplineGraph: