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This is done with a process of limits. Average rate of change is, for example, (change of y) / (change of x). If you make "change of x" smaller and smaller, in theory (with certain assumptions, a bit too technical to mention here), you get closer and closer to the instant rate of change. In the "limit", when "change of x" approaches zero, you get the true instantaneous rate of change.

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The instantaneous rate of change is the limiting value of the average change as the time period is made smaller and smaller.

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Q: How does average change help find instant rate of change in math?
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