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Mathematics
Problem
Let
g
g
g
be continuous on
[
2
,
8
]
[2,8]
[
2
,
8
]
and differentiable on
(
2
,
8
)
(2,8)
(
2
,
8
)
. Suppose
g
′
(
x
)
=
0
g'(x)=0
g
′
(
x
)
=
0
only at
x
=
5
x=5
x
=
5
, and
g
′
′
(
5
)
>
0
g''(5)>0
g
′′
(
5
)
>
0
. Explain briefly why
x
=
5
x=5
x
=
5
is where
g
g
g
attains its absolute minimum on
[
2
,
8
]
[2,8]
[
2
,
8
]
.
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