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instantaneous rate of change

The rate of change at a single instant — the limit of average rates over shrinking intervals.

The instantaneous rate of change of f at x=a is \displaystyle\lim_{h \to 0} \dfrac{f(a+h)-f(a)}{h}, the derivative f'(a) — what the average rate of change approaches as the interval shrinks to a single point.

Examples

  • A speedometer reading is the instantaneous rate of change of position with respect to time.

See also

average rate of change derivative limit
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