Let f(x) be a continuous function on I=[a,b], and let g(x) be a differentiable function on I. Let g(a)=0 and c≠0 a constant. Prove that if

|g(x) f(x)+c g′(x)|≤|g(x)| for all x∈I,

then g(x)=0 for all x∈I.

The best solution was submitted by Seungkyun Park (박승균), 수리과학과 2008학번. Congratulations!

Here is his Solution of Problem 2011-18.

Alternative solutions were submitted by 김범수 (수리과학과 2010학번, +3), 장경석 (2011학번, +3),  김태호 (2011학번, +2), 김재훈 (EEWS대학원, +2).