Extreme Value Theorem, Extrema, Critical Points
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
Identify the critical points of
f
(
x
)
=
x
3
3
−
x
f(x) = \frac{x^3}{3} - x
f
(
x
)
=
3
x
3
−
x
.
QUESTION
Determine the global extrema of
f
(
x
)
=
−
x
2
+
4
x
f(x) = -x^2 + 4x
f
(
x
)
=
−
x
2
+
4
x
on
[
0
,
4
]
[0, 4]
[
0
,
4
]
.
QUESTION
State the Second Derivative Test.
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ANSWER
Use
f
′
′
(
x
)
f''(x)
f
′′
(
x
)
to determine concavity and local extrema. Evaluate second derivative at critical points.
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