# How does instantaneous rate of change differ from average rate of change?

Instantaneous rate of change is essentially the value of the derivative at a point; in other words, it is the slope of the line tangent to that point. Average rate of change is the slope of the secant line passing through two points; it gives the average rate of change across an interval.

Below is a graph showing a function,

#(Deltay)/(Deltax) = (f(4) - f(2))/(4 - 2)#

is the average rate of change of

Below is a graph showing the function

#dy/dx = f'(2) = 2*2 = 4# ,and it is the instantaneous rate of change at the point

#(2,4)# .

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Instantaneous rate of change refers to the rate of change of a function at a specific point, typically calculated by finding the derivative of the function at that point. Average rate of change, on the other hand, refers to the overall rate of change of a function over a given interval, calculated by finding the slope of the secant line between two points on the function. In summary, instantaneous rate of change focuses on a single point, while average rate of change considers the change over an interval.

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