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Mathematics
Problem
For
g
(
x
)
=
x
4
−
4
x
2
+
1
g(x)=x^{4}-4x^{2}+1
g
(
x
)
=
x
4
−
4
x
2
+
1
, the critical numbers are
x
=
−
2
,
0
,
2
x=-\sqrt{2},\,0,\,\sqrt{2}
x
=
−
2
,
0
,
2
. Which of the following correctly ranks the corresponding function values from least to greatest? a)
g
(
−
2
)
<
g
(
0
)
<
g
(
2
)
g(-\sqrt{2})<g(0)<g(\sqrt{2})
g
(
−
2
)
<
g
(
0
)
<
g
(
2
)
b)
g
(
−
2
)
=
g
(
2
)
<
g
(
0
)
g(-\sqrt{2})=g(\sqrt{2})<g(0)
g
(
−
2
)
=
g
(
2
)
<
g
(
0
)
c)
g
(
0
)
<
g
(
−
2
)
=
g
(
2
)
g(0)<g(-\sqrt{2})=g(\sqrt{2})
g
(
0
)
<
g
(
−
2
)
=
g
(
2
)
d)
g
(
2
)
<
g
(
−
2
)
<
g
(
0
)
g(\sqrt{2})<g(-\sqrt{2})<g(0)
g
(
2
)
<
g
(
−
2
)
<
g
(
0
)
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