This is an picture of the basins of attraction to the roots when
Newton's method is applied to the equation *x*^3 - 1 = 0 in
the complex plain. The center of the picture is the origin and the
real axis, i.e,. the *x*-axis runs from -2 to 2 in the
picture. The roots are 1 and
-1/2 + *i*3^(1/2)/2 and -1/2 - *i*3^(1/2)/2. If you start
with any point in the blue area and apply Newton's method, the iterates
will converge to 1.

From the picture you can see that most of the negative real axis is blue
except for a few points like the origin. See if you can find the coordinates
of the first point on the negative real axis to the left the origin
not in the blue area. In other words find the largest *x* < 0
whose iterates do not converge to 1.

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