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Derivative as Instantaneous Rate of Change in Calculus

The derivative f'(t) is the limit of the average rate of change of f over an interval as the interval shrinks to zero, giving the instantaneous rate at a single instant. After learning this a student can read f'(t) as "how fast the quantity is changing right now", interpret its sign as growth or decay, and recognise when a described process is stated as a rate rather than as a total. They can also read and interpret an equation that relates a quantity's rate of change to the quantity itself.

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Epsilon-N Definition of the Limit of a Sequence in Real Analysis

Instantaneous rate of change describes how a function is changing at a single point, in contrast to average rate of change, which requires two points; because a single point yields an indeterminate 0…