Introduction to Optimization Problems
AP Calculus AB · Flashcards · Application
AP CALCULUS AB · FLASHCARDS
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QUESTION
Find the derivative of
f
(
x
)
=
x
e
x
f(x) = x \text{e}^x
f
(
x
)
=
x
e
x
.
QUESTION
Find the critical points of
f
(
x
)
=
x
2
−
4
x
+
4
f(x) = x^2 - 4x + 4
f
(
x
)
=
x
2
−
4
x
+
4
.
QUESTION
Identify the critical points of
f
(
x
)
=
x
3
−
3
x
2
f(x) = x^3 - 3x^2
f
(
x
)
=
x
3
−
3
x
2
.
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ANSWER
Critical points at
x
=
0
x = 0
x
=
0
and
x
=
2
x = 2
x
=
2
. Setting
f
′
(
x
)
=
3
x
2
−
6
x
=
3
x
(
x
−
2
)
=
0
f'(x) = 3x^2 - 6x = 3x(x-2) = 0
f
′
(
x
)
=
3
x
2
−
6
x
=
3
x
(
x
−
2
)
=
0
.
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