lim as h->0 of (f(x+h) - f(x))/h
or
lim as x->a of (f(x) - f(a))/(x - a)
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Instantaneous speed is the speed at a particular moment in time.The average speed of an object tells you the (average) rate at which it covers distance
Suppose you accelerate in your car from stopped to 50 km.hr-1. When you were stopped your instantaneous speed was zero. At the end of the period of acceleration your instantaneous speed was 50 km.hr-1. If your rate of acceleration was constant then your average speed was 25 km.hr-1.
The concept of average speed is somewhat simpler than "instantaneous speed".
It is the instantaneous speed in the direction in which the displacement is measured.
The instantaneous speed is the gradient of the graph at that particular point.