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Mathematics
Problem
Define
f
q
(
x
)
=
1
x
2
+
q
f_q(x)=\dfrac{1}{x^{2}+q}
f
q
(
x
)
=
x
2
+
q
1
for all real
x
x
x
satisfying
x
2
+
q
≠
0
x^{2}+q\neq 0
x
2
+
q
=
0
. For which values of
q
q
q
is
f
q
f_q
f
q
concave up for every
x
x
x
in its domain? a)
q
<
0
q<0
q
<
0
b)
q
>
0
q>0
q
>
0
c)
q
=
0
q=0
q
=
0
d)
q
≤
0
q\le 0
q
≤
0
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