Rates of Change
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
is stationary therefore y is stationary.
If the height of the helicopter is increasing,
If the height of the helicopter is decreasing,
The height of the helicopter is increasing.