Newton's Method

I have the function f(x) = e^(sin^(3)x) + x^6 − 2x^4 − x^3 − 1 on the interval [-2, 2]. I have plotted this and found that the roots are (to 6 decimal places) -1.197623, 0.000000 and 1. 530133. I have to determine which of these roots converge quadratically with Newton's method, and also find the multiplicity of the roots that converge only linearly with Newton's method.

Any tips or explanations for this would be incredibly appreciated. Thanks!