Your undamped Newton's method throws you from x = 0.5 to x = 46 appr. in the next step. Here, your function cannot be evaluated because of the large exp() term.
Conclusion: Newton's method doesn't converge in all cases.
Try a different initial point x0 in the region where the function is steeper than in 0.5 (e.g. 0.9).
Or use a damping factor 0 < d < 1:
x = x0-d*f(x0)/fd(x0);
Convergence will be slower, but safer.
Further, you should also check whether abs(f(x)) is really small when you break the iteration. abs(x-x0) < tol usually doesn't suffice for the iteration to be converged if your function is steep.
