Intuitively the rate of change of something is the rate of change
with respect to time:
The acceleration is the rate of change of velocity with respect to
time.
The velocity is the rate of change of distance with respect to
time.
In general we have a quantity that is a function of time and we
find the rate of change of that quantity by differentiating with
respect to time. For example
A model helicopter takes off from a point O at timeand
moves vertically so that its
height,cm,
above O after timeseconds
is given by
1) Find the rate at which the height is increasing.
2) Verify thathas
a stationary value whenand
determine whether this stationary
value is a maximum value or a minimum value.
3) Find the rate of change ofwith
respect towhen
4) Determine whether the height of the helicopter aboveis
increasing or decreasing at
the instant when
1)
2)When
is
stationary therefore y is stationary.
3)
When
4)
If the height of the helicopter is increasing,
If the height of the helicopter is decreasing,
When
The height of the helicopter is increasing.
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