Please use MatLab and comment code. df(x) Problem 3: two-point central differenc

Question

Please use MatLab and comment code.

df(x) Problem 3: two-point central difference formula: df (x) foh0-h) ?? 2h where h is a small number relative to xo. Write a user-defined function function that calculates the derivative of a math function f(x) by using the two-point central difference formula. For the user-defined function name, use dfdx= Funder (Func, X0), where Funcis a name for the function that is passed into Funder, and x0 is the point where the derivative is calculated. Use h-xo/100 in the two-point central difference formula. Write a script to use the user-defined function Funder to calculate the following: (a) The derivative of f(x)x3e2* at xo 0.6 (b) The derivative off(x) at x,-2.5 The script will also compare the answer obtained from Funder with the analytical solution (use format long) using the following definition of the relative error AnswerFromFunder AnalyticalDerivativel AnalyticalDerivative RelError-

Explanation / Answer

PLEASE CREATE FILE test_funder.m AND PASTE BELOW CODE

close all

clear all

clc

%a) f = x^3e^2x

f = @(x) x^3 * exp(2 * x)

x0 = 0.6;

df_by_dx = Funder(f,x0)

%b) f = 3^x/x^2

f1 = @(x) 3^x / x^2

x0 = 2.5;

df1_by_dx = Funder(f1,x0)

PLEASE CREATE FILE Funder.m AND PASTE BELOW CODE

function dfdx = Funder(Fun,x0)

%find h with given formula as h = x0/100;

h = x0 / 100;

% x0 + h

x0_plus_h = x0 + h;

%x0 - h

x0_minus_h = x0 - h;

%f(x0 + h)

f_a = feval(Fun,x0_plus_h);

%f(x0 - h)

f_b = feval(Fun,x0_minus_h);

%df(x)/dx = f(x0 + h) - f(x0 - h) / 2h

dfdx = (f_a - f_b) / (2 * h);

PLEASE REFER BELOW OUTPUT

f =

function_handle with value:

@(x)x^3*exp(2*x)

df_by_dx =

5.0209

f1 =

function_handle with value:

@(x)3^x/x^2

df1_by_dx =

0.7448

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