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Mathematics
Mathematics
Problem
Let
f
f
f
and
g
g
g
be differentiable on
[
0
,
5
]
[0,5]
[
0
,
5
]
with
f
′
(
x
)
>
g
′
(
x
)
f'(x)>g'(x)
f
′
(
x
)
>
g
′
(
x
)
for
0
<
x
<
5
0<x<5
0
<
x
<
5
and
f
(
0
)
=
g
(
0
)
f(0)=g(0)
f
(
0
)
=
g
(
0
)
. Explain what can be concluded about the sign of
f
(
x
)
−
g
(
x
)
f(x)-g(x)
f
(
x
)
−
g
(
x
)
for
0
<
x
≤
5
0<x\le 5
0
<
x
≤
5
.
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