Unformatted text preview: Other rates of change Given y = f ( x ), let: • 4 x = x 2x 1 : the change in x from x 1 to x 2 . • 4 y = f ( x 2 )f ( x 1 ): the corresponding change in y . Then, the average rate of change of y with respect to x over the interval [ x 1 , x 2 ] is: 4 y 4 x = f ( x 2 )f ( x 1 ) x 2x 1 Let 4 x → 0, the limit of the average rates of change = the (instantaneous) rate of change of y with respect to x at x = x 1 : lim 4 x → 4 y 4 x = lim x 2 → x 1 f ( x 2 )f ( x 1 ) x 2x 1 Notice : average rate = change in y divided by the change in x ⇒ the instantaneous rate of change (at x 1 ) can be thought as how much the function y = f ( x ) is changing at the point x 1 . Example 6 of Section 2.7 (textbook): 1...
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 Fall '08
 Noohi
 Calculus, Derivative, Slope, Ms. Hoa Nguyen

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