```{code-cell} ipython3

:tags: [raises-exception]

attempt = 1

for init in initLs:

for attempt, init in enumerate(initLs, start=1):

print(f"Attempt {attempt}: Starting value is {init} \n")

%time p = newton(lambda p: e(p, A, b, c), init, tol=1e-15, max_iter=15)

print("-" * 64)

attempt += 1

```

We can see that Newton's method may fail for some starting values.

Sometimes it may take a few initial guesses to achieve convergence.

Substitute the result back to the formula to check our result

Substitute the result back to the formula to check our result using the second initial guess which converges

```{code-cell} ipython3

e(p, A, b, c)

p_solution = newton(lambda p: e(p, A, b, c), initLs[1], tol=1e-15, max_iter=15)

e(p_solution, A, b, c)

```

We can see the result is very accurate.