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Sharon Evans

Published on June 30, 2014

Section 3-4, 2 Math 1433 Online Lecture Notes Example 1: For 3 ) ( x x f = : (a) Find the average rate of change of ) ( x f if x changes from 1 to 4. Note that the above is the same as the slope of the secant line through )) 1 ( , 1 ( f and )) 4 ( , 4 ( f . Example 2: The profit (in dollars) from the sale of x iPods is given by x x x P 80 ) ( 2 + − = . Find the average rate of change of profit if production increases from 20 iPods to 30 iPods. Explain the meaning of this value in the context of the problem. Instantaneous Rate of Change Consider the function ) ( x f y = shown in the graph below. Draw the secant line between the points )) ( , ( a f a and )) ( , ( h a f h a + + . Suppose h is getting closer to a value of 0. Draw a series of secant lines that illustrates h becoming smaller and smaller. ) ( h a f + Definition: Instantaneous Rate of Change Instantaneous rate of change of ) ( x f at a x = : Instantaneous rate of change is also known as the slope of the _____________________________ line. ) ( a f