Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem A. 634. (January 2015)

A. 634. Let $\displaystyle n\ge2$ be a in integer and let $\displaystyle f\colon \mathbb{R}\to[-1,1]$ be an $\displaystyle n$ times differentiable function. Show that the equation $\displaystyle f^{(n)}(x)=0$ has at least $\displaystyle n-1$ distinct solutions.

(5 pont)

Deadline expired on February 10, 2015.

### Statistics:

 7 students sent a solution. 5 points: Janzer Barnabás, Williams Kada. 4 points: Fehér Zsombor, Szabó 789 Barnabás. 3 points: 1 student. 2 points: 1 student. 0 point: 1 student.

Problems in Mathematics of KöMaL, January 2015