Answer:
Check below, please
Step-by-step explanation:
Hello!
1) In the Newton Method, we'll stop our approximations till the value gets repeated. Like this

2) Looking at the graph, let's pick -1.2 and 3.2 as our approximations since it is a quadratic function. Passing through theses points -1.2 and 3.2 there are tangent lines that can be traced, which are the starting point to get to the roots.
We can rewrite it as: 

As for

3) Rewriting and calculating its derivative. Remember to do it, in radians.


For the second root, let's try -1.5

For x=-3.9, last root.

5) In this case, let's make a little adjustment on the Newton formula to find critical numbers. Remember their relation with 1st and 2nd derivatives.



For -1.2

For x=0.4

and for x=-0.4

These roots (in bold) are the critical numbers