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13142023-13-Average-Rates-of-Change

# 13142023-13-Average-Rates-of-Change - Math 135 Class Notes...

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Math 135 Business Calculus Spring 2009 Class Notes 1.3 Average Rates of Change Consider a function y = f ( x ) and two input values x 1 and x 2 . The change in input , or the change in x , is x 2 x 1 . The corresponding change in output , or the change in y , is y 2 y 1 = f ( x 2 ) f ( x 1 ) . DEFINITION OF AVERAGE RATE OF CHANGE The average rate of change of y = f ( x ) with respect to x , as x changes from x 1 to x 2 , is the ratio of the change in output to the change in input: y 2 y 1 x 2 x 1 = f ( x 2 ) f ( x 1 ) x 2 x 1 where x 1 6 = x 2 . If we look at the graph of the function, then the average rate of change will equal the slope of the line passing through the points P ( x 1 , y 1 ) and Q ( x 2 , y 2 ). The line passing through P and Q is called a secant line . EXAMPLE The graph in the figure shows a typical response to adversing. Aftr an amount a is spent on advertising, the company sells N ( a ) units of a product. Find the average rate of change of N as a changes a) from 0 to 1 b) from 1 to 2 c) from 2 to 3 0 1 2 3 4 a 0 100 200 300 400 500 600 700

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