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Mathematics
Mathematics
Problem
Let
g
(
x
)
=
tan
x
−
2
x
g(x)=\tan x-2x
g
(
x
)
=
tan
x
−
2
x
on the interval
(
−
π
2
,
π
2
)
\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)
(
−
2
π
,
2
π
)
. On which open subinterval(s) of this domain is
g
g
g
increasing? a)
(
−
π
2
,
−
π
4
)
\left(-\dfrac{\pi}{2},-\dfrac{\pi}{4}\right)
(
−
2
π
,
−
4
π
)
and
(
π
4
,
π
2
)
\left(\dfrac{\pi}{4},\dfrac{\pi}{2}\right)
(
4
π
,
2
π
)
b)
(
−
π
4
,
π
4
)
\left(-\dfrac{\pi}{4},\dfrac{\pi}{4}\right)
(
−
4
π
,
4
π
)
c)
(
π
4
,
π
2
)
\left(\dfrac{\pi}{4},\dfrac{\pi}{2}\right)
(
4
π
,
2
π
)
d) everywhere on
(
−
π
2
,
π
2
)
\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)
(
−
2
π
,
2
π
)
except at
x
=
0
x=0
x
=
0
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