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Mathematics
Mathematics
Problem
Consider the function
f
k
(
x
)
=
x
3
+
3
k
x
2
+
5
f_k(x)=x^{3}+3kx^{2}+5
f
k
(
x
)
=
x
3
+
3
k
x
2
+
5
, where
k
∈
R
k\in\mathbb{R}
k
∈
R
. For which value(s) of
k
k
k
is
f
k
f_k
f
k
increasing on the entire real line? a)
k
>
0
k>0
k
>
0
b) \text{all real }k c)
k
=
0
k=0
k
=
0
d)
k
<
0
k<0
k
<
0
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