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Rates of Change

5.2 Rates of Change, Motion in a Straight Line

Finding Rates of Change

  • Recall that by definition, y=f^{\prime}(x) also represents the instantaneous rate of change of a function.
  • Also, by definition, the average rate of change across an interval [a,\ b] is given by

Average \: Rate \: of \: Change =\frac{f(b)-f(a)}{b-a}

  • Using differentiation, we can find the rate of change of a variable (e.g. volume, temperature, speed etc.) at any certain point of another variable (e.g. time).

Example

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