Solving Optimization Problems
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
Find the maximum area of a rectangle with perimeter of 20.
QUESTION
Find the critical points of
f
(
x
)
=
2
x
3
−
9
x
2
+
12
x
−
3
f(x) = 2x^3 - 9x^2 + 12x - 3
f
(
x
)
=
2
x
3
−
9
x
2
+
12
x
−
3
.
QUESTION
What is the critical point of
f
(
x
)
=
4
x
2
−
4
x
f(x) = 4x^2 - 4x
f
(
x
)
=
4
x
2
−
4
x
?
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ANSWER
Critical point:
x
=
1
2
x = \frac{1}{2}
x
=
2
1
. Solve
f
′
(
x
)
=
8
x
−
4
=
0
f'(x) = 8x - 4 = 0
f
′
(
x
)
=
8
x
−
4
=
0
to get
x
=
1
2
x = \frac{1}{2}
x
=
2
1
.
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