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Mathematics
Problem
Let
f
(
x
)
=
e
2
x
−
3
x
f(x)=e^{2x}-3x
f
(
x
)
=
e
2
x
−
3
x
and
g
(
x
)
=
x
3
−
6
x
g(x)=x^{3}-6x
g
(
x
)
=
x
3
−
6
x
. On which of the following intervals are both
f
f
f
and
g
g
g
increasing simultaneously? a)
(
−
2
,
2
)
(-\sqrt{2},\sqrt{2})
(
−
2
,
2
)
b)
(
−
∞
,
−
2
)
∪
(
2
,
∞
)
(-\infty,-\sqrt{2})\cup(\sqrt{2},\infty)
(
−
∞
,
−
2
)
∪
(
2
,
∞
)
c)
(
2
,
∞
)
(\sqrt{2},\infty)
(
2
,
∞
)
d)
(
1
2
ln
(
3
2
)
,
2
)
\left(\frac{1}{2}\ln\!\left(\frac{3}{2}\right),\,\sqrt{2}\right)
(
2
1
ln
(
2
3
)
,
2
)
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