3.4
Derivative as a Rate of Change
Recall that the derivative
=
instantaneous rate of change.
f
0
(
x
o
) = lim
h
→
0
f
(
x
0
+
h
)

f
(
x
0
)
h
provided this limit exists.
From here on, when we say "
rate of change", we mean the
instantaneous rate of change.
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3.4
Derivative as a Rate of Change
Recall that the derivative
=
instantaneous rate of change.
f
0
(
x
o
) = lim
h
→
0
f
(
x
0
+
h
)

f
(
x
0
)
h
provided this limit exists.
From here on, when we say "
rate of change", we mean the
instantaneous rate of change.
Example:How fast is the area of a circle increasing (with respect tothe radius) when the radius is8ft?
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Linear Motion: Position Function, Velocity and Speed
Suppose an object is moving along a coordinate line where its
position at time
t
is described by a function
s
=
f
(
t
)
, called the
position function
.