Mean Value Theorem
AP Calculus AB · Flashcards · Application
AP CALCULUS AB · FLASHCARDS
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QUESTION
Find the
c
c
c
for
f
(
x
)
=
1
x
2
f(x) = \frac{1}{x^2}
f
(
x
)
=
x
2
1
on
[
1
,
3
]
[1, 3]
[
1
,
3
]
using the Mean Value Theorem.
QUESTION
Identify the value
c
c
c
guaranteed by the Mean Value Theorem for
f
(
x
)
=
x
2
f(x)=x^2
f
(
x
)
=
x
2
on
[
1
,
3
]
[1, 3]
[
1
,
3
]
.
QUESTION
Determine
c
c
c
for
f
(
x
)
=
x
2
f(x)=x^2
f
(
x
)
=
x
2
on
[
3
,
6
]
[3, 6]
[
3
,
6
]
using the Mean Value Theorem.
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ANSWER
c
=
4.5
c = 4.5
c
=
4.5
. Set
f
′
(
c
)
=
2
c
f'(c) = 2c
f
′
(
c
)
=
2
c
equal to
36
−
9
6
−
3
=
9
\frac{36-9}{6-3} = 9
6
−
3
36
−
9
=
9
, so
c
=
4.5
c = 4.5
c
=
4.5
.
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