Chapter 4.9, Problem 444E

Newton’s method can be used to find maxima and minima of functions in addition to the roots. In this case apply Newton's method to the derivative function $f\text{'}\left(x\right)$ to find its roots, instead of the original function. For the following exercises, consider the formulation of the method.

444. Minimum of $f\left(x\right)=x^2\sin x$ , closest non-zero minimum to x = 0