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Mathematics
Problem
Consider
h
a
(
x
)
=
ln
(
1
+
a
x
2
)
h_a(x)=\ln(1+a x^{2})
h
a
(
x
)
=
ln
(
1
+
a
x
2
)
with
a
>
0
a>0
a
>
0
. Determine the set of all positive values of
a
a
a
for which
h
a
h_a
h
a
is concave up on the interval
(
−
1
,
1
)
(-1,1)
(
−
1
,
1
)
.
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