Suppose that
f
\displaystyle {f}
f
is a function with
f
′
(
8
)
=
0
\displaystyle {f}'{\left({8}\right)}={0}
f
′
(
8
)
=
0
and
f
′
′
(
8
)
=
4
\displaystyle {f}{''}{\left({8}\right)}={4}
f
′′
(
8
)
=
4
.
Then
f
\displaystyle {f}
f
has a relative maximum at
x
=
8
\displaystyle {x}={8}
x
=
8
.
Then
f
\displaystyle {f}
f
has a relative minimum at
x
=
8
\displaystyle {x}={8}
x
=
8
.
Given this information, we cannot determine whether
f
\displaystyle {f}
f
has a maximum or a minimum at
x
=
8
\displaystyle {x}={8}
x
=
8
.
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