Find each root to two decimal places using newtons

Question

Question: Suppose you want to find a solution of the equation

x³ + 3x² + 3x - 6 = 0

Consider f(x) = x³ + 3x² + 3x - 6.

(a) Find f'(x), and use it to show that f(x) increases everywhere.

(b) How many roots does the original equation have?

(c) For each root, find an interval which contains it.

(d) Find each root to two decimal places, using Newton's method.