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Omni-MATH / Today, Ivan the Confessor prefers continuous functions f:[0,1]→R satisfying f(x)+f(y)≥|x−y| for all pairs x,y∈[0,1]. Find the minimum of ∫₀¹f over all preferred functions. (

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problem

Today, Ivan the Confessor prefers continuous functions f:[0,1]→Rf:[0,1]\to\mathbb{R} satisfying f(x)+f(y)≥|x−y|f(x)+f(y)\geq |x-y| for all pairs x,y∈[0,1]x,y\in [0,1]. Find the minimum of ∫01f\int_0^1 f over all preferred functions. (
Plain-text mathematical notation (without MathML)
Today, Ivan the Confessor prefers continuous functions f:[0,1]→R satisfying f(x)+f(y)≥|x−y| for all pairs x,y∈[0,1]. Find the minimum of ∫₀¹f over all preferred functions.

(
Original LaTeX notation
Today, Ivan the Confessor prefers continuous functions $f:[0,1]\to\mathbb{R}$ satisfying $f(x)+f(y)\geq |x-y|$ for all pairs $x,y\in [0,1]$. Find the minimum of $\int_0^1 f$ over all preferred functions.

(

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Source and history

task_id
5da2e356-f76e-5cf8-917b-dce686867174
task_key
test--5da2e356-f76e-5cf8-917b-dce686867174
task_revision_id
1
config / split
/ test

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