Changes > Average change
123Average change

Theory

The graph shows a part of the graph of the function y = x 2 .

The average change of the function f on the interval [ 2 , 5 ] is:


Δ y Δ x = y ( 5 ) y ( 2 ) 5 2 = 5 2 2 2 5 2 = 7

This ratio of the difference between the outcomes of the function at the boundaries of the interval and the difference of the corresponding `x` -values is called the difference quotient of the function on the interval [ 2 , 5 ] .

In the graph the difference quotient is equal to the slope of the line through A ( 2 , 4 ) and B ( 5 , 25 ) .
This line is called the chord AB.

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