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f(x^3) - \sqrt3 /3 x^6 increases - All-Russian MO 2003 Regional (R4) 11.3

Source:

September 17, 2024

algebraIncreasing

Problem Statement

The functions

f(x)-x

and

f(x^2)-x^6

are defined for all positive

x

and increase. Prove that the function

f(x^3) -\frac{\sqrt3}{2} x^6

also increases for all positive

x