f(x)=1+x21 Consider a data set of n equidistant points on the graph of f(x) on the interval [5,5]. That is, {(x1,f(x1)),(x2,f(x2)),,(xn,f(xn))} with x1=5 and xn=5. Write a MATLAB function y= newton_interp (n,x) that computes the value(s) of the Newton interpolating polynomial p(x) for this data at x(x can be a scalar or a vector), where n is the number of data points. (Refer to the algorithm at the bottom of page 331.) (b) Let x=5:1/30:5 and write a program to call the function newton_interp (n,x) with n=5,10, and 15 and plot the graphs of three interpolating polynomials and the exact function on the same figure. You may find hold on function useful to plot multiple graphs in the same figure. Add the legends to the figure. (c) Discuss your observation on the error behaviors depending on the number of data points. f(x)=1+x21 Consider a data set of n equidistant points on the graph of f(x) on the interval [5,5]. That is, {(x1,f(x1)),(x2,f(x2)),,(xn,f(xn))} with x1=5 and xn=5. Write a MATLAB function y= newton_interp (n,x) that computes the value(s) of the Newton interpolating polynomial p(x) for this data at x(x can be a scalar or a vector), where n is the number of data points. (Refer to the algorithm at the bottom of page 331.) (b) Let x=5:1/30:5 and write a program to call the function newton_interp (n,x) with n=5,10, and 15 and plot the graphs of three interpolating polynomials and the exact function on the same figure. You may find hold on function useful to plot multiple graphs in the same figure. Add the legends to the figure. (c) Discuss your observation on the error behaviors depending on the number of data points