Working With the Intermediate Value Theorem
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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QUESTION
Does
f
(
x
)
=
cos
(
x
)
f(x) = \text{cos}(x)
f
(
x
)
=
cos
(
x
)
satisfy IVT on
[
0
,
3
π
2
]
[0, \frac{3\text{π}}{2}]
[
0
,
2
3
π
]
,
N
=
0
N = 0
N
=
0
?
QUESTION
Is
N
=
0
N = 0
N
=
0
reachable for
f
(
x
)
=
x
2
−
1
f(x) = x^2 - 1
f
(
x
)
=
x
2
−
1
on
[
0
,
2
]
[0, 2]
[
0
,
2
]
?
QUESTION
Identify the key feature of a function for IVT applicability.
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ANSWER
Continuity on the interval
[
a
,
b
]
[a, b]
[
a
,
b
]
. No gaps or jumps ensure all intermediate values between endpoints exist.
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