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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
(
arctan
x
)
3
+
(
arccot
x
)
3
f(x) = (\arctan x)^3 + (\operatorname{arccot} x)^3
f
(
x
)
=
(
arctan
x
)
3
+
(
arccot
x
)
3
. If the range of
f
(
x
)
f(x)
f
(
x
)
is
[
a
,
b
]
[a, b]
[
a
,
b
]
, then find the value of
b
7
a
\frac{b}{7a}
7
a
b
.
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