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Your function has argument order func, deri, start, iters but you are calling it with start, func, deri, iters... By changing it I got

sage: newMet(tf, x, 1.)
1.41421356237310

which looks like $\sqrt(2)$.

Your function has argument order func, deri, start, iters but you are calling it with start, func, deri, iters... By changing it I got

sage: newMet(tf, x, 1.)
1.41421356237310

which looks like $\sqrt(2)$.$\sqrt{2}$.