If possible, can someone please help me fix this function so I can find the roots of a certain function?

In the attachments is a picture of my function. I am trying to write a function that will find the roots of a function given an initial guess "x". I want to make a while statement so the function keeps on repeating until the function gets the correct value of x, such that the tolerance is 1*10^-10. If anyone can help me it'll be greatly appreciated.

NOTE: I was trying to mimic my professors code. The first code is mine with the function f(x)=sin(x)+[(2e^(x/10)*cos(x)]-3 and the initial guess x is 5. The solution should be outputting x ≈ 5.91061140513925.

My professors code is below mine with the function f(E) = E-esin(E)-M; where e is eccentricity. His initial guess is the value of M.

MY CODE FUNCTION

% fx4 = root(x)

function fx4 = root(x)

MAXITER = 100; % in case the loop does not converge

TOL = 1e-10; % tolerance for convergence

x4 = 5; % first guess

fx4 = sin(x)+(2*exp(x/10)*cos(x))-3; % f(x) that we want to be zero

iter = 1; % count the iterations

while ( abs(fx4) > TOL )

fx4 = sin(x)+(2*exp(x/10)*cos(x))-3;

iter = iter+1;

if (iter>=MAXITER)

error('Did not converge');

exit

end

end

end

MY Professors CODE

% E = keplersolve(M,e)

function E = keplersolve(M,e)

MAXITER = 100; % in case the loop does not converge

TOL = 1e-11; % tolerance for convergence

En = M; % first guess

fn = En - e*sin(En) - M; % f(E) that we want to be zero

iter = 1; % count the iterations

while ( abs(fn) > TOL )

En = En - fn/(1-e*cos(En));

fn = En - e*sin(En) - M;

iter = iter+1;

if (iter>=MAXITER)

error('Did not converge');

exit

end

end

E = En

end

[OCDER]

How are you adjusting and using x4 in your code per iteration? Also, use the {}Code button in this Matlab Answer text box to make your code more readable like this :

TOL = 1e-10;
x4 = 5; % first guess ** BUT, This is not used and updated per loop! **
fx4 = sin(x)+(2*exp(x/10)*cos(x))-3;
iter = 1;