Rate of change


Rates of change occur in many practical applications. Generally, if x and y are quantities related by an equation y = f (x). There is a distinction between the average rate of change, represented by the slope of the secant line, and the instantaneous rate of change, represented by the slope of the tangent line.
We consider the average rate of change at decreasing intervals, making x2 tend to x1, and hence tend to zero. The limit of the average rates of change is called the instantaneous rate of change of y in relation to x, and is described by:


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