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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
x
3
+
k
x
2
f(x)=x^{3}+k x^{2}
f
(
x
)
=
x
3
+
k
x
2
, where
k
k
k
is a real constant. Determine all real values of
k
k
k
for which
f
f
f
is concave up for every
x
>
0
x>0
x
>
0
in its domain.
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