f(x) = (x^2 - 1)^2
f'(x) = 4·x·(x^2 - 1) = 4·x^3 - 4·x
g(x) = - (x^2 - 1)·(x + 1)
g'(x) = - 3·x^2 - 2·x + 1
Stellen mit gleicher Steigung
f'(x) = g'(x)
4·x^3 - 4·x = - 3·x^2 - 2·x + 1
4·x^3 + 3·x^2 - 2·x - 1 = 0
Eine Nullstelle bei -1 --> Polynomdivision
(4·x^3 + 3·x^2 - 2·x - 1) / (x + 1) = 4·x^2 - x - 1
4·x^2 - x - 1 = 0
x = 1/8 ± √17/8