Not a tangent!

Not a tangent!

Move either green point. Observe what happens when x=0 or x=1.

Tangent lines never cross a curve.

f(x) = (x - 1)^(1 / 3) + 1
D = Point(f)
f'(x) = 1 / ((3 * (x - 1)^(2 / 3)))
slope: f'(x(D))
intercept: y(D) - (slope * x(D))
t(x) = (slope * x) + intercept
E: (x(D) - 0.2, t(x(D) - 0.2))
F: (x(D) + 0.2, t(x(D) + 0.2))
c = Segment(E, F)
g(x) = x^(3)
A = Point(g)
a = Tangent(A, g)
B: (x(A) - 0.2, a(x(A) - 0.2))
C: (x(A) + 0.2, a(x(A) + 0.2))
b = Segment(B, C)
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