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I need to find the "black points" (where the function becomes undefined) of an equation x^3 -1 (newtons cubic). Is there a solve function for this?

I need to find the "black points" (where the function becomes undefined) of an equation x^3 -1 (newtons cubic). Is there a way to solve a function for this?

I need to find the "black points" (where the function becomes undefined) of an equation x^3 -1 (newtons cubic). Is there a way to solve a function for this?

I need to find the "black points" (where the function becomes undefined) of an equation x^3 -1 (newtons cubic). using newtons method. So the function turns out to be F(x) = x - (x^3-1)/(3x^2). Is there a way to solve find a function for this?majority of the points (where x is undefined as in the Newton cubic fractal photo aka the black points) using Sage?