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Prove
f
(
x
)
=
1
x
is concave down on the open interval
(
−
∞
,
0
)
and concave up on the open interval
(
0
,
∞
)
.
Prove that
f
(
x
)
=
x
has no concavity.
Prove
x
3
is concave down on the interval
(
−
∞
,
0
)
and concave up on the interval
(
0
,
∞
)
.
Prove that
f
(
x
)
=
x
2
is concave up.
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Lesson Specific Problems
Prove
f
(
x
)
=
1
x
is concave down on the open interval
(
−
∞
,
0
)
and concave up on the open interval
(
0
,
∞
)
.
Prove that
f
(
x
)
=
x
has no concavity.
Prove
x
3
is concave down on the interval
(
−
∞
,
0
)
and concave up on the interval
(
0
,
∞
)
.
Prove that
f
(
x
)
=
x
2
is concave up.