Finding the roots of equation by newton-raphson method?

Write a MATLAB program which utilizes Newton-Raphson method to determine the smallest positive root of the following function:

x^3 – e ^-x = 0.5

i did this but the answer is wrong.. could you please help me about the wrong step?

this is my answer;

x(1)=0;
i=1;
for i=i+1
    f(i)=x(i)^3-exp(-x(i))-0.5;
    df(i)=3*x(i)^2+exp(-x(i));
    x(i+1)=x(i)-(f(i)/df(i));
end
disp(x(end))

[Torsten]

for i=1:100, e.g., instead of for i=i+1

[Asli]

to be sure

x^3 – e ^-x = 0.5

this is my function and i said x(1)=0 is that true?

thank you!!

[James Tursa]

x(1)=0 is simply your starting guess which you can choose. From the wording of the assignment you posted it looks like you can pick this yourself.

[Asli]

thank you so much!!! its much clear now

Answer 1

[Ibrahim Mohammed Wajid]

In your code, the for loop is not exactly a loop. It is confined only for one value i = 2.

You can update for i = i + 1 to for i = 1:100 (say) so that your for loop runs for 100 times.