Chapter 4.9, Problem 437E

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.

437. What additional restrictions are necessary on the function f ?

For the following exercises, use Newton’s method to find the location of the local minima and/or maxima of the following functions; round to three decimals.