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