Mean Value Theorem
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Determine if
f
(
x
)
=
∣
x
∣
f(x) = |x|
f
(
x
)
=
∣
x
∣
satisfies the Mean Value Theorem on
[
−
1
,
1
]
[-1, 1]
[
−
1
,
1
]
.
QUESTION
For
f
(
x
)
=
x
4
f(x) = x^4
f
(
x
)
=
x
4
, determine
c
c
c
on
[
−
1
,
1
]
[-1, 1]
[
−
1
,
1
]
using the Mean Value Theorem.
QUESTION
Find
c
c
c
for
f
(
x
)
=
x
2
f(x) = x^2
f
(
x
)
=
x
2
over
[
1
,
3
]
[1, 3]
[
1
,
3
]
using the Mean Value Theorem.
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ANSWER
c
=
2
c = 2
c
=
2
. Set
f
′
(
c
)
=
2
c
=
9
−
1
3
−
1
=
4
f'(c) = 2c = \frac{9-1}{3-1} = 4
f
′
(
c
)
=
2
c
=
3
−
1
9
−
1
=
4
, so
c
=
2
c = 2
c
=
2
.
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