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Soros Olympiad in Mathematics
VI Soros Olympiad 1999 - 2000 (Russia)
11.2
f''(0) , (...((x - 2)^2 - 2)^2 - 2)^2..- VI Soros Olympiad 1999-00 Round 1 11.2
f''(0) , (...((x - 2)^2 - 2)^2 - 2)^2..- VI Soros Olympiad 1999-00 Round 1 11.2
Source:
May 21, 2024
algebra
derivative
calculus
Problem Statement
Let
f
(
x
)
=
(
.
.
.
(
(
x
−
2
)
2
−
2
)
2
−
2
)
2
.
.
.
−
2
)
2
f(x) = (...((x - 2)^2 - 2)^2 - 2)^2... - 2)^2
f
(
x
)
=
(
...
((
x
−
2
)
2
−
2
)
2
−
2
)
2
...
−
2
)
2
(here there are
n
n
n
brackets
(
)
( )
(
)
). Find
f
′
′
(
0
)
f''(0)
f
′′
(
0
)
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