MathDB

There exists x_0 and y_0

Source: Baltic Way 1999

December 23, 2010

quadraticstrigonometryalgebra proposedalgebra

Problem Statement

For all positive real numbers

x

and

y

let

f(x,y)=\min\left( x,\frac{y}{x^2+y^2}\right)

Show that there exist

x_0

and

y_0

such that

f(x, y)\le f(x_0, y_0)

for all positive

x

and

y

, and find

f(x_0,y_0)

.

Back to Problems View on AoPS