Question

Solve using MATLAB and provide code please

4. The first derivative of a function f(x) at a point x = xo can be approximated with the four-point central difference formula: dx 12h where h is a small number relative to xo. Write a user-defined function function that calculates the derivative of a math function fx) by using the four-point central difference formula. For the user-defined function name, use dfax-FoPrder(Fun, x0), where Fun is a name for the function that is passed into FoPtder, and x0 is the point where the derivative is calculated. Use h =-in the four-point central difference formula. 100 3 2x 4a (10 points) Compute the derivative of the function f(x) at x0-0.6 using the FoPtder function. Test it in the command window (use format long) 4.b (10 points) Repeat 4.a but with anonymous function. 4.c (5 points) Find the equation for the derivative of f(x) and the value at 0.6. Compare the result with the value in part (a) Ad (10 points) Compute the derivative of the function g(x) =-atx0-2.5 using the FoPtder function. Test it in the command window (use format long) 4.e (5 points) Find the equation for the derivative of g(x) and the value at 2.5. Compare the result with the value in part (d)

Answer 1

%%% Matlab function

function dfdx = FoPtdr(Fun,x0)
h=x0/100;
dfdx=(Fun(x0-2*h)-8*Fun(x0-h)+8*Fun(x0+h)-Fun(x0+2*h))/(12*h);
end

%%%% Test

clc;
close all;
clear all;
format long;
Fun=@(x) x^3*exp(2*x);
x0=0.6;

(a)

>> FoPtdr(Fun,x0)

ans =

5.020016698059604

>>

(b)

>> Fun=@(x) x^3;
>> x0=2;
>> FoPtdr(Fun,x0)

ans =

12.000000000000027

(c)

%%%

syms x;
f=x^3*exp(2*x);
df=subs(diff(f),x0);
fprintf('Actual value = %f Error =%1.10f \n',df,abs(x1-df));

OUTPUT:

Actual value = 5.020017 Error =0.0000000891   
>>

(d) and (e)

clc;
close all;
clear all;
format long;
Fun=@(x) 3^x/x^2;
x0=2.5;
x1=FoPtdr(Fun,x0);
fprintf('Using function FoPtdr dydx=%f \n',x1);
syms x;
f=3^x/x^2;
df=subs(diff(f),x0);
fprintf('Actual value = %f Error =%1.10f \n',df,abs(x1-df));

OUTPUT:

Using function FoPtdr dydx=0.744785
Actual value = 0.744785 Error =0.0000000174   
>>