Determining Intervals on Increasing, Decreasing Functions
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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QUESTION
What is the second derivative of
f
(
x
)
=
x
3
−
3
x
2
+
2
x
f(x) = x^3 - 3x^2 + 2x
f
(
x
)
=
x
3
−
3
x
2
+
2
x
?
QUESTION
Find intervals where
f
(
x
)
=
x
2
−
8
x
+
15
f(x) = x^2 - 8x + 15
f
(
x
)
=
x
2
−
8
x
+
15
is increasing.
QUESTION
How can you determine the critical points of
f
(
x
)
=
x
3
−
6
x
2
f(x) = x^3 - 6x^2
f
(
x
)
=
x
3
−
6
x
2
?
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ANSWER
Solve
f
′
(
x
)
=
0
f'(x) = 0
f
′
(
x
)
=
0
:
x
=
0
,
4
x = 0, 4
x
=
0
,
4
.
f
′
(
x
)
=
3
x
2
−
12
x
=
3
x
(
x
−
4
)
f'(x) = 3x^2 - 12x = 3x(x-4)
f
′
(
x
)
=
3
x
2
−
12
x
=
3
x
(
x
−
4
)
, set equal to zero.
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