## 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 time and moves vertically so that its

height, cm, above O after time seconds is given by 1) Find the rate at which the height is increasing.

2) Verify that has a stationary value when and determine whether this stationary

value is a maximum value or a minimum value.

3) Find the rate of change of with respect to when 4) Determine whether the height of the helicopter above is 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. 