Extreme Value Theorem, Extrema, Critical Points
AP Calculus AB · Flashcards · Application
AP CALCULUS AB · FLASHCARDS
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QUESTION
Determine the global extrema of
f
(
x
)
=
−
x
2
f(x) = -x^2
f
(
x
)
=
−
x
2
on
[
−
1
,
1
]
[-1, 1]
[
−
1
,
1
]
.
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
]
.
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ANSWER
Global max at
x
=
2
x = 2
x
=
2
; global min at
x
=
0
,
4
x = 0, 4
x
=
0
,
4
. Vertex of parabola at
x
=
2
x = 2
x
=
2
gives maximum.
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