# Solution: 2015-21 Differentiable function

Assume that a function $$f : (0, 1) \to [0, \infty)$$ satisfies $$f(x) = 0$$ at all but countably many points $$x_1, x_2, \cdots$$. Let $$y_n = f(x_n)$$. Prove that, if $$\sum_{n=1}^{\infty} y_n < \infty$$, then $$f$$ is differentiable at some point.

The best solution was submitted by Jang, Kijoung (장기정, 수리과학과 2014학번). Congratulations!

Here is his solution of problem 2015-21.

Alternative solutions were submitted by 박성혁 (수리과학과 2014학번, +3), 이종원 (수리과학과 2014학번, +3), 최인혁 (2015학번, +3), 신준형 (2015학번, +2).

GD Star Rating