Solution: 2022-19 Inequality for twice differentiable functions

Let f:RR be a twice differentiable function satisfying f(0)=0 and 0f(x)1. Prove that
(10f(x)dx)210[f(x)]3dx.

The best solution was submitted by 기영인 (KAIST 22학번, +4). Congratulations!

Here is the best solution of problem 2022-19.

Other solutions were submitted by 여인영 (KAIST 물리학과 20학번, +3), Kawano Ren (Kaisei Senior High School, +3), 최예준 (서울과기대 행정학과 21학번, +3), 김준성 (KAIST 물리학과 박사과정, +3).

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