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Mathematics
Mathematics
Problem
A differentiable function
f
f
f
is defined on the closed interval
[
2
,
6
]
[2,6]
[
2
,
6
]
and satisfies
f
′
(
x
)
≥
3
f'(x)\ge 3
f
′
(
x
)
≥
3
for every
x
x
x
in
(
2
,
6
)
(2,6)
(
2
,
6
)
. a. (i) Explain why
f
(
2
)
<
f
(
4
)
<
f
(
6
)
f(2)<f(4)<f(6)
f
(
2
)
<
f
(
4
)
<
f
(
6
)
must hold. b. (ii) Show that
f
(
6
)
−
f
(
2
)
≥
12
f(6)-f(2)\ge 12
f
(
6
)
−
f
(
2
)
≥
12
, clearly indicating each logical step used.
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