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All-Russian Olympiad Regional Round
2003 All-Russian Olympiad Regional Round
11.3
11.3
Part of
2003 All-Russian Olympiad Regional Round
Problems
(1)
f(x^3) - \sqrt3 /3 x^6 increases - All-Russian MO 2003 Regional (R4) 11.3
Source:
9/17/2024
The functions
f
(
x
)
−
x
f(x)-x
f
(
x
)
−
x
and
f
(
x
2
)
−
x
6
f(x^2)-x^6
f
(
x
2
)
−
x
6
are defined for all positive
x
x
x
and increase. Prove that the function
f
(
x
3
)
−
3
2
x
6
f(x^3) -\frac{\sqrt3}{2} x^6
f
(
x
3
)
−
2
3
x
6
also increases for all positive
x
x
x
.
algebra
Increasing