SOLUTION: Given the function f(x) = x^2 - x find the AVERAGE RATE of CHANGE of f from 3 to 5

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Start with the given equation.


Plug in


Square 3 to get 9


Subtract


So the point (3,6) is on the graph


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Start with the given equation.


Plug in


Square 5 to get 25


Subtract


So the point (5,20) is on the graph


So the average rate of change from x=3 to x=5 is simply the slope of the line that goes through the points (3,6) and (5,20)


So let's find the slope of the line that goes through the points (3,6) and (5,20)


Start with the slope formula.


Plug in , , , and


Subtract from to get


Subtract from to get


Reduce


So the slope of the line that goes through the points and is

Since the slope is 7, this means that the average rate of change from x=3 to x=5 is 7