Use Newton's Method with the equation x3 − b = 0 to derive the following formula for the cube root: xn + 1 = 1 3 2xn + b xn 2 . Let f(x) = x3 − b. Then the formula for Newton's method yields xn + 1 = xn − f(xn) f '(xn) = xn − xn 3 − b xn2 = 2xn + b xn2 .