For x >0, consider the equation

x+ lnx= 0

Implement the secant method and find the root of the above equation. Usex0= 0.5, x1= 0.6 and|xk+1xk|<10^-10 as a convergence criterion. In addition, use your function from Question 5 employing Newtons method and repeat the

Calculation with same initial guess x0 and convergence criterion as before. Finally, attach your code for the secant method and provide MATLAB outputs for both

cases. Which method converges faster? Briefly explain

(Question 5: Implement Newtons method in MATLAB. In particular, create a function, which utilizes the method, and store it as an m-file. Then, use your function to estimate

7 by finding the positive root off(x) =x²7. Try two different initial guesses: (i)x0= 2 and (ii)x0= 500 and consider|xk+1xk|<10^-10as a convergence criterion.

Attach your codes and provide MATLAB output for both cases)