Use MATLAB to implement newton's divided-difference formula

ALGORITHM Newton's Divided-Difference Formula 3.2 To obtain the divided-difference coefficients of the interpolatory polynomial P on the (n+1) distinct numbers xo, xi. . Xn for the function f: INPUT numbers xo. xi.... xn; values f(xo), f(af(x OUTPUT the numbers Foo. Fi where as Fo,o. Fo.., Fn.o Step 1 For i = 1,2, ,n or = 1, 2, set F i.j--F xi-xi-j Step 2 OUTPUT (Fo.o, Fi. . Fn m); STOP Write a MATLAB function to implement the Newton's divided difference formula in Algorithm 3.2. Note that the index should run from 1 instead of 0 that is used in the textbook. This is because MATLAB does not allow index 0 Your function should use the same order of input below. Note that we do not return F as in the algorithm. Instead we calculate the interpolated function value at function y-newton (X,Y,x) %X=numbers x 1 x 2 x n % Y = values f (x 1) f (x 2) f (x n) % x = interpolation point x % y- interpolated function value at x, i.e. P(x) your implementation below end Save your function in 'newton.m', and interpolate the tabular function given below at the point x 0.05 f(x) 0.0 0.1 0.3 0.6 -5.89483 -5.65014 .17788 -4.28172 Your function should return -5.9487. Now, add the point x 1.1, f(x)-3.99583 to the table, and interpolate the tabular function at x-1.05. Your function should return -4.1423