MathDB
|f'(x) - f'(y)| <= 4|x-y| , differentiable

Source: Polish MO Second Round 1972 p6

September 8, 2024
algebracalculus

Problem Statement

Prove that there exists a function f f defined and differentiable in the set of all real numbers, satisfying the conditions f(x)f(y)4xy|f'(x) - f'(y)| \leq 4|x-y|.