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Mathematics
Mathematics
Problem
On the interval
0
≤
x
≤
7
0 \le x \le 7
0
≤
x
≤
7
, a differentiable function
h
h
h
satisfies the following about its derivative: •
h
′
(
x
)
>
0
h'(x) > 0
h
′
(
x
)
>
0
for
0
<
x
<
2
0 < x < 2
0
<
x
<
2
and
5
<
x
<
7
5 < x < 7
5
<
x
<
7
•
h
′
(
x
)
=
0
h'(x) = 0
h
′
(
x
)
=
0
at
x
=
2
x = 2
x
=
2
and
x
=
5
x = 5
x
=
5
•
h
′
(
x
)
<
0
h'(x) < 0
h
′
(
x
)
<
0
for
2
<
x
<
5
2 < x < 5
2
<
x
<
5
Determine the
x
x
x
-coordinate(s) at which
h
h
h
attains a local maximum on
(
0
,
7
)
(0,7)
(
0
,
7
)
.
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