Newton's Method is a technique for approximating a root to an equation of the form \(f(x)=0\). What is required is an initial estimate for the root, called \(x_1 ...

Explain why Newton's method fails to find the root no matter which initial approximation \(x_1\not=0\) is used. Illustrate your explanation with a sketch. Suppose \(k\) is a constant. Show that if we ...