Rates of Change in Applied Concepts
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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QUESTION
Determine the rate of change for
f
(
x
)
=
x
2
f(x) = x^2
f
(
x
)
=
x
2
at
x
=
5
x = 5
x
=
5
.
QUESTION
Evaluate the derivative of
f
(
x
)
=
1
x
f(x) = \frac{1}{x}
f
(
x
)
=
x
1
at
x
=
1
x = 1
x
=
1
.
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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