Rates of Change in Applied Concepts
AP Calculus BC · Flashcards · Recall
AP CALCULUS BC · FLASHCARDS
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QUESTION
What is the derivative of a constant function
f
(
x
)
=
c
f(x) = c
f
(
x
)
=
c
?
QUESTION
What is the derivative of
f
(
x
)
=
a
x
f(x) = a^x
f
(
x
)
=
a
x
where
a
a
a
is a constant?
QUESTION
Find the rate of change of the volume of a sphere with respect to its radius.
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ANSWER
d
V
d
r
=
4
π
r
2
\frac{dV}{dr} = 4\pi r^2
d
r
d
V
=
4
π
r
2
. Derivative of
V
=
4
3
π
r
3
V = \frac{4}{3}\pi r^3
V
=
3
4
π
r
3
using power rule.
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