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Unformatted text preview: 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) units of a product....
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