Determining Intervals on Increasing, Decreasing Functions
AP Calculus AB · Flashcards · Application
AP CALCULUS AB · FLASHCARDS
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QUESTION
Find
f
′
(
x
)
f'(x)
f
′
(
x
)
for
f
(
x
)
=
4
x
3
−
9
x
2
+
6
x
−
1
f(x) = 4x^3 - 9x^2 + 6x - 1
f
(
x
)
=
4
x
3
−
9
x
2
+
6
x
−
1
.
QUESTION
Compute the derivative of
f
(
x
)
=
x
2
+
4
x
−
5
f(x) = x^2 + 4x - 5
f
(
x
)
=
x
2
+
4
x
−
5
.
QUESTION
Find
f
′
(
x
)
f'(x)
f
′
(
x
)
given
f
(
x
)
=
5
x
3
−
2
x
+
7
f(x) = 5x^3 - 2x + 7
f
(
x
)
=
5
x
3
−
2
x
+
7
.
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ANSWER
f
′
(
x
)
=
15
x
2
−
2
f'(x) = 15x^2 - 2
f
′
(
x
)
=
15
x
2
−
2
. Apply power rule:
(
5
x
3
)
′
=
15
x
2
(5x^3)' = 15x^2
(
5
x
3
)
′
=
15
x
2
and
(
−
2
x
)
′
=
−
2
(-2x)' = -2
(
−
2
x
)
′
=
−
2
.
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