Mean Value Theorem
AP Calculus AB · Flashcards · Recall
AP CALCULUS AB · FLASHCARDS
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QUESTION
Explain why
f
(
x
)
=
∣
x
∣
f(x) = |x|
f
(
x
)
=
∣
x
∣
does not satisfy Mean Value Theorem on
[
−
1
,
1
]
[-1, 1]
[
−
1
,
1
]
.
QUESTION
What conditions must be met to apply the Mean Value Theorem?
QUESTION
What is the derivative expression found using Mean Value Theorem?
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ANSWER
f
′
(
c
)
=
f
(
b
)
−
f
(
a
)
b
−
a
f'(c) = \frac{f(b)-f(a)}{b-a}
f
′
(
c
)
=
b
−
a
f
(
b
)
−
f
(
a
)
. This is the core equation of the Mean Value Theorem.
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