Can someone please explain how to solve for this using MatLab 2. Exercise Let\'s

Question

Can someone please explain how to solve for this using MatLab

2. Exercise Let's differentiate the following function: f(x) e -2x+1 f'(x) = ??? What is the first derivative of this function at x- 1? Now, numerically evaluate the approximate first derivative of this function at x = 1 by: (a) Forward finite difference method, using an interval of h = 0.1 (b) Backward finite difference method, using an interval of h = 0.1 (c) Centered finite difference method, using an interval of h = 0.1 Calculate the error of each method by comparing the numerical derivative with the result from calculus method (above

Explanation / Answer

clc;

clear all;

close all;

disp('Manual Differentiation of f (x) = (e^x)? 2x +1 :')

disp('first_derivative = (e^x)-2');

x=1;

disp('The first derivative of given function at x = 1:');

first_derivative_manual_value = exp(x)-2;

disp(first_derivative_manual_value);

disp('Numerical Evaluation of f (x) = (e^x)?2x +1 :');

h=0.1;

fd=(f(x+h)-f(x))/h;

cd=(f(x+(h/2))-f(x-(h/2)))/h;

bd=(f(x)-f(x-h))/h;

err1=first_derivative_manual_value-fd;

err2=first_derivative_manual_value-cd;

err3=first_derivative_manual_value-bd;

disp('forward difference derivative and error');

disp(fd);

disp(err1);

disp('central difference derivative and error');

disp(cd);

disp(err2);

disp('backward difference derivative and error');

disp(bd);

disp(err3);

// add function in another command line //

function [ y ] = f(x)

y=exp(x)-2*x +1;

end

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