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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
tan
x
−
x
f(x)=\tan x - x
f
(
x
)
=
tan
x
−
x
for
−
π
2
<
x
<
π
2
-\dfrac{\pi}{2}<x<\dfrac{\pi}{2}
−
2
π
<
x
<
2
π
. On which of the following intervals is
f
f
f
increasing? a)
(
−
π
2
,
0
)
\left(-\dfrac{\pi}{2},0\right)
(
−
2
π
,
0
)
only b)
(
0
,
π
2
)
\left(0,\dfrac{\pi}{2}\right)
(
0
,
2
π
)
only c)
(
−
π
2
,
0
)
\left(-\dfrac{\pi}{2},0\right)
(
−
2
π
,
0
)
and
(
0
,
π
2
)
\left(0,\dfrac{\pi}{2}\right)
(
0
,
2
π
)
d)
f
f
f
is not increasing on any subinterval of
(
−
π
2
,
π
2
)
\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)
(
−
2
π
,
2
π
)
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