Question

#use MATLAB script

1)  Calculate the following for the function f(x) = e^-4x- 2x³ 

a. Calculate the derivative of the function by hand. Write a MATLAB function that calculates the derivative 05. of this function and calculate the derivative at x = 0.5. 

b. Develop an M- to evaluate the cetered finite-difference approximation (use equation below), at x = 0.5. Assume that h = 0.1. 

c. Repeat part (b) for the second-order forward and backward differences. Again Assume that h = 0.1. 

d. Using the results obtained in parts b and c, calculate the percentage error between the actual value and the results of (b) and (c). 

Answer 1

clc
clear all
close all
f=@(x) exp(-4*x)-2*x^3;
g=matlabFunction(diff(sym(f)));
disp('Exact value of derivative at x=0.5 is');
ex=g(0.5);
disp(ex);
disp('Value for part b');
h=0.1;
x=0.5;
Df1=(-f(x+2*h)+8*f(x+h)-8*f(x-h)+f(x-2*h))/(12*h)
disp('Value for part c, forward difference');
Df2=(-f(x+2*h)+4*f(x+h)-3*f(x))/(2*h)
disp('Value for part c, backward difference');
Df3=(3*f(x)-4*f(x-h)+f(x-2*h))/(2*h)
disp('Percent error in central difference is');
abs(ex-Df1)/abs(ex)*100
disp('Percent error in forward difference is');
abs(ex-Df3)/abs(ex)*100
disp('Percent error in backard difference is');
abs(ex-Df2)/abs(ex)*100