Rate of Change at a Point
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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QUESTION
Find the average rate of change of
f
(
x
)
=
x
2
f(x) = x^2
f
(
x
)
=
x
2
from
x
=
1
x = 1
x
=
1
to
x
=
3
x = 3
x
=
3
.
QUESTION
What is the instantaneous rate of change of
f
(
x
)
=
ln
(
x
)
f(x) = \text{ln}(x)
f
(
x
)
=
ln
(
x
)
at
x
=
1
x = 1
x
=
1
?
QUESTION
What is the derivative of
f
(
x
)
=
x
3
f(x) = x^3
f
(
x
)
=
x
3
at
x
=
2
x = 2
x
=
2
?
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ANSWER
12
12
12
. Using power rule:
f
′
(
x
)
=
3
x
2
f'(x) = 3x^2
f
′
(
x
)
=
3
x
2
, so
f
′
(
2
)
=
12
f'(2) = 12
f
′
(
2
)
=
12
.
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