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Problem
Problem
Let
F
(
x
)
=
1
+
f
(
x
)
+
(
f
(
x
)
)
2
+
(
f
(
x
)
)
3
F(x) = 1 + f(x) + (f(x))^2 + (f(x))^3
F
(
x
)
=
1
+
f
(
x
)
+
(
f
(
x
)
)
2
+
(
f
(
x
)
)
3
, where
f
(
x
)
f(x)
f
(
x
)
is an increasing differentiable function and
F
(
x
)
=
0
F(x) = 0
F
(
x
)
=
0
has a positive root, then a.
F
(
x
)
F(x)
F
(
x
)
is an increasing function b.
F
(
0
)
≤
0
F(0) \le 0
F
(
0
)
≤
0
c.
f
(
0
)
≤
−
1
f(0) \le -1
f
(
0
)
≤
−
1
d.
F
′
(
0
)
>
0
F'(0) > 0
F
′
(
0
)
>
0
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