haif - part of the problem (of why you are getting stuck in an infinite loop) is due to
dx=0.1;
epsi=0.01;
Xi=0.1; % <----- set here only
Xm=4.0;
F = @(x) 1+5.25*x-sec(sqrt(0.68*x));
a=Xi; % <------ a initialized to Xi
f1=F(a);
b=a+dx;
f2=F(a)
while a<Xm
a=Xi; % <------ a reset to static Xi
On each iteration of the loop, the code is always re-assigning a to Xi and since the latter is only set outside the loop, then we are always repeating the same iteration again and again. Try commenting out this line and re-running your code. You'll probably also have a problem with
disp ('function approaching infinity at ',a);
with a "too many input arguments" error. Just change this to
disp (sprintf('function approaching infinity at %f',a));
