Let
f
(
x
,
y
)
=
y
2
−
2
x
2
y
+
4
x
3
+
20
x
2
. The only critical points are
(
−
2
,
4
)
,
(
0
,
0
)
, and
(
5
,
25
)
. Which of the following correctly describes the behavior of f at these points? Source: Society of Actuaries.
a.
(
−
2
,
4
)
: local (relative) minimum
(
0
,
0
)
: local (relative) minimum
(
5
,
25
)
: local (relative) maximum
b.
(
−
2
,
4
)
: local (relative) minimum
(
0
,
0
)
: local (relative) maximum
(
5
,
25
)
: local (relative) maximum
c.
(
−
2
,
4
)
: neither a local (relative) minimum nor local (relative) maximum
(
0
,
0
)
: local (relative) maximum
(
5
,
25
)
: local (relative) minimum
d.
(
−
2
,
4
)
: local (relative) maximum
(
0
,
0
)
: neither a local (relative) minimum nor local (relative) maximum
(
5
,
25
)
: local (relative) minimum
e.
(
−
2
,
4
)
: neither a local (relative) minimum nor local (relative) maximum
(
0
,
0
)
: local (relative) minimum
(
5
,
25
)
: neither a local (relative) minimum nor local (relative) maximum