Rate of change

Average rate of change measures how much a function changes over an interval: for f(x) = x^2 from x = 1 to x = 3, that is (9 - 1) / (3 - 1) = 4. Instantaneous rate of change zooms into a single point: checking narrower and narrower intervals starting at x = 1 (like 1 to 1.1, then 1 to 1.01) gives slopes approaching 2, and that limiting value is the instantaneous rate at x = 1.

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