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Mathematics
Mathematics
Problem
For
a
>
0
a>0
a
>
0
, define
f
a
(
x
)
=
x
4
−
4
a
x
2
f_a(x)=x^{4}-4a x^{2}
f
a
(
x
)
=
x
4
−
4
a
x
2
on the interval
[
−
2
,
2
]
[-2,2]
[
−
2
,
2
]
. For which of the following values of
a
a
a
does
f
a
f_a
f
a
attain its absolute maximum value at the endpoints
x
=
−
2
x=-2
x
=
−
2
and
x
=
2
x=2
x
=
2
rather than at an interior point of the interval? a)
1.5
1.5
1.5
b)
3
3
3
c)
0.5
0.5
0.5
d)
1
1
1
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