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Mathematics
Problem
A function
f
f
f
is continuous on
[
1
,
4
]
[1,4]
[
1
,
4
]
and differentiable on
(
1
,
4
)
(1,4)
(
1
,
4
)
. If
∣
f
′
(
x
)
∣
≤
3
|f'(x)|\le 3
∣
f
′
(
x
)
∣
≤
3
for all
x
x
x
in
(
1
,
4
)
(1,4)
(
1
,
4
)
, what is the greatest possible value of
∣
f
(
4
)
−
f
(
1
)
∣
|f(4)-f(1)|
∣
f
(
4
)
−
f
(
1
)
∣
? a)
12
12
12
b)
9
9
9
c)
3
3
3
d)
6
6
6
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