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Mathematics
Problem
For the family
f
p
(
x
)
=
x
4
−
4
x
3
+
p
x
2
f_p(x)=x^{4}-4x^{3}+p x^{2}
f
p
(
x
)
=
x
4
−
4
x
3
+
p
x
2
, determine all real values of
p
p
p
such that
f
p
f_p
f
p
is concave up on the interval
(
1
,
∞
)
(1,\infty)
(
1
,
∞
)
.
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