Question

Please answer this problem using MATLAB.

Problem 4 : Finite difference formula and interpolation For this problem, you will approximate the derivative of the function g(x)5x6x 23823x 15 on a set of points using the centered difference formula (x +h) -g(x- h) 2h g'(x) Then, you will find the interpolating polynomial through these points, Q, and verify that it is indeed close to the polynomial that is the true derivative of g, ie. Q(x) g'(x) 25x 24x36x+16x+3 In your prob40 . Define a vector x with 5 elements Xi,i = 1,--, 5, so that they are evenly spaced in [-2,2] . For each noole xi, approxmate g'(m) using the centered difference formula (1) with h 0.01. Store these approximations in anot her vector y Find the interpolating polynomial Q for the data in vectors x and y using polyfit Output: Suppress all output and comment all fprintf messages from intermediate steps and function calls, and MATH353, Spring 2019 Assignment 7 (a) Plot the interpolating polynomial Q and the true derivative of g in -2,2] in the same figure with different line styles. Add a legend. (b) Print the coefficients of Qin the standard output. (c) Make a comment explaining why it is not surprising that these coefficients are close to the coefficients of

Answer 1

`Hey,

Note: Brother in case of any queries, just comment in box I would be very happy to assist all your queries

clc
clear all
x=linspace(-2,2,5);
y=[];
g=@(x) 5*x^5+6*x^4-2*x^3+8*x^2+3*x-15;
h=0.01;
for i=1:length(x)
y(i)=(g(x(i)+h)-g(x(i)-h))/(2*h);
end
C=polyfit(x,y,4);
gd=@(x) 25*x^4+24*x^3-6*x^2+16*x+3;
fplot(gd,[-2,2]);
xx=-2:0.01:2;
hold on;
plot(xx,polyval(C,xx));
fprintf('Coefficients of polynomial are: %f*x^4+%f*x^3%f*x^2+%f*x+%f',C);
legend('Analytical','Finite difference');
disp('Both are approximately same since this is a polynomial fit for centered difference with low h');

MATLAB R2018a Figure Search Documentation Log In EDITOR naertfEile Edit View Insert Iools Desktop Wndow Help Find Files Compare ▼ Print GoTo▼ Comment New Open Save Find 600 Analytical -Finite difference C: Users PRADEEP KALRA 、Documents Current Folder 500 Name- mathlab E 400 in New folder a1.m 300 200 A1.dat A1.mat A2.dat A3.dat New to 100 ce, properly vectorize your function to return 0.5 0 0.5 1.5 Name ▲ Value In matlab.graphics.unction. FunctionLine tsingleFplot (ine 234) @(x)5"X ^ 5+ 6"X 4.2.. @(x)25% ^4-24*.3-... 0.0100 In 1 (1ine 193) tvectorizeFplot (line 193) In tplot (line 163) In saveee (line 12 1-2.-1,0,1,21 x401 double 155.0150,-17.99762. fg coefficients of polynomial 25.000000 "X^ 4 +24.000000 "X^ 3-5.995000"Х"2+16.002 400"X+2.999800>> are: sp ENG 4:00 AM US 04/22/19 O Type here to search

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