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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Question 154214: Given the function f(x) = x^2 - x find the AVERAGE RATE of CHANGE of f from 3 to 5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+x%5E2+-+x Start with the given equation.


f%283%29+=+%283%29%5E2+-+3 Plug in x=3


f%283%29+=+9+-+3 Square 3 to get 9


f%283%29+=+6 Subtract


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


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f%28x%29+=+x%5E2+-+x Start with the given equation.


f%285%29+=+%285%29%5E2+-+5 Plug in x=5


f%285%29+=+25+-+5 Square 5 to get 25


f%285%29+=+20 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)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%2820-6%29%2F%285-3%29 Plug in y%5B2%5D=20, y%5B1%5D=6, x%5B2%5D=5, and x%5B1%5D=3


m=%2814%29%2F%285-3%29 Subtract 6 from 20 to get 14


m=%2814%29%2F%282%29 Subtract 3 from 5 to get 2


m=7 Reduce


So the slope of the line that goes through the points and is m=7

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