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