MathDB

1

Part of 1998 IberoAmerican Olympiad For University Students

Problems(1)

Integral f^2,g^2=1 => f(c)+g(c)<=2 - OIMU 1998 Problem 1

Source:

9/12/2010
The definite integrals between 00 and 11 of the squares of the continuous real functions f(x)f(x) and g(x)g(x) are both equal to 11. Prove that there is a real number cc such that f(c)+g(c)≤2f(c)+g(c)\leq 2
calculusintegrationfunctioninequalitiesreal analysisreal analysis unsolved