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Mathematics
Mathematics
Problem
Let
g
g
g
be continuous on
[
2
,
7
]
[2,7]
[
2
,
7
]
and differentiable on
(
2
,
7
)
(2,7)
(
2
,
7
)
with
∣
g
′
(
x
)
∣
≤
6
|g'(x)|\le 6
∣
g
′
(
x
)
∣
≤
6
for all
x
x
x
in
(
2
,
7
)
(2,7)
(
2
,
7
)
. Which of the following must be true? a)
∣
g
(
7
)
−
g
(
2
)
∣
≤
6
|g(7)-g(2)|\le 6
∣
g
(
7
)
−
g
(
2
)
∣
≤
6
b) There exists
c
∈
(
2
,
7
)
c\in(2,7)
c
∈
(
2
,
7
)
such that
∣
g
′
(
c
)
∣
=
6
|g'(c)|=6
∣
g
′
(
c
)
∣
=
6
c)
∣
g
(
7
)
−
g
(
2
)
∣
≤
30
|g(7)-g(2)|\le 30
∣
g
(
7
)
−
g
(
2
)
∣
≤
30
d)
∣
g
(
7
)
−
g
(
2
)
∣
=
30
|g(7)-g(2)|=30
∣
g
(
7
)
−
g
(
2
)
∣
=
30
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