What does average rate of change mean in calculus?


The average rate of change of a continuous function, ##f(x)## , on the closed interval ## [a, b]## is given by

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Basically, the average rate of change tells us how, on average, the y-value of a function is changing per unit change in the x-value.

The average rate of change formula is just a variation of the slope formula


since ## y = f(x)##.

Let’s let ##f(x)=-x^2+8x-9##.

The average rate of change on the closed interval ##[2,5]## is given by


This is also the slope of the secant line to the graph of ##f## through the points ##(2,3)## and ##(5,6)##

See image below.

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