KöMaL problem A, 2015

Algebra Difficulty 6.0 National Olympiad Prove it Hungary

Let $n\ge2$ be a in integer and let $f\colon \mathbb{R}\to[-1,1]$ be an $n$ times differentiable function. Show that the equation $f^{(n)}(x)=0$ has at least $n-1$ distinct solutions.
(5 pont)

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