Show that Newton's method applied to$\displaystyle x^{n} - c = 0$ (where n and c are positive constants) produces the iterative scheme $\displaystyle x_{n+1} =\frac{1}{n}[(n-1)x_n + cx_n^{1-n}]$ for approximating $\displaystyle c^{\frac{1}{n}}$. We learned Newton's method, but we haven't applied it to "schemes" and my teacher told us to look at this problem tonight. Can someone explain, please! Thanks.