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Mathematics
Mathematics
Problem
Consider
f
m
(
x
)
=
x
3
−
3
m
x
2
f_m(x)=x^{3}-3mx^{2}
f
m
(
x
)
=
x
3
−
3
m
x
2
on the interval
[
0
,
4
]
[0,4]
[
0
,
4
]
. Find all real numbers
m
m
m
for which the absolute minimum of
f
m
f_m
f
m
occurs at an interior critical point rather than at an endpoint.
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