The expressions given above apply only when the rate of change is constant or when only the average (mean) rate of change is required. If the velocity or positions change non- linearly over time, such as in the example shown in the figure, then differentiation provides the correct solution. Differentiation reduces the time-spans used above to be extremely small (infinitesimal) and gives a velocity or acceleration at each point on the graph rather than between a start and end point. The derivative forms of the above equations are