Newton's Method for initial approximation

Question

In order to find an approximation to the root of the equation $-x^3-\cos x=0$ by using Newton's method, which of the following initial approximations can be chosen? $x_0=1 , x_0=0, x_0=2 , x_0=1$ or $x_0=0$ and $x_0=1$ Which one?

Answer 1

If you plot the function, you will see that the only solution is $x\approx-0.865474$. Try all of these initial values in your code and you will see, what happens. In one case it converges however only if the damped Newton is used.