2. Consider the function f(x)-sin2(x) in the interval [0,2 You are given the following 4 points of this function: 0 | 0.75 0.75 2n| 0 (a) (4 points) Calculate the cubic Lagrange interpolating polynomial as the sum of the Lo(x)f(xo), L1(x)f(xi), L2(x) f(x2), Ls(x)f(z3) polynomials we defined in class. The final answer should be in the form P(x) ax3+bx2+cx+d, but with a, b, c, d known. [Note: if any the coefficients are 0 you do not need to include the term in the final polynomial. DELIVERABLES: All your work in constructing the polynomial. This is to be done by hand not MATLAB (b) (2 points) Plot f(z) = sin2(x) in the interval 0,2 by creating vectors [0 : 0 . 1 : 2*pi] ; x = =sin(x).^2; y Use hold on to retain the plot and plot the four data points provided above as stars DELIVERABLES: The commands and the resulting plot from MATLAB. from part (a) DELIVERABLES: The commands and the resulting plot from MATLAB (c) (2 points) On the same graph as part (b) plot the interpolating polynomial P(x)