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

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.