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Problem
Problem
Let
f
:
(
0
,
∞
)
→
(
0
,
∞
)
f: (0, \infty) \to (0, \infty)
f
:
(
0
,
∞
)
→
(
0
,
∞
)
be a derivable function and
F
(
x
)
F(x)
F
(
x
)
is the primitive of
f
(
x
)
f(x)
f
(
x
)
such that
2
(
F
(
x
)
−
f
(
x
)
)
=
f
2
(
x
)
2(F(x) - f(x)) = f^2(x)
2
(
F
(
x
)
−
f
(
x
))
=
f
2
(
x
)
for any real positive
x
x
x
a.
f
f
f
is strictly increasing b.
lim
x
→
∞
f
(
x
)
x
=
1
\lim_{x \to \infty} \frac{f(x)}{x} = 1
lim
x
→
∞
x
f
(
x
)
=
1
c.
f
f
f
is strictly decreasing d.
f
f
f
is non-monotonic
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