Unformatted text preview: y/ Δ x for our function y = f ( x ) = √ 625x 2 when x changes from 7 to 7 . 1. Here Δ x = 7 . 17 = 0 . 1 is the change in x , and Δ y = f ( x + Δ x )f ( x ) = f (7 . 1)f (7) = p 6257 . 1 2p 6257 2 ≈ 23 . 970624 =. 0294 . Thus, Δ y/ Δ x ≈ . 0294 / . 1 =. 294. This means that y changes by less than one third the change in x , so apparently y is not very sensitive to changes in x at x = 7. We say “apparently” here because we don’t really know what happens between 7 and 7 . 1. Perhaps y changes dramatically as x runs through the values from 7 to 7 . 1, but at 7 . 1 y 19...
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 Spring '07
 JonathanRogawski
 Math, Calculus, Derivative, Rate Of Change, Slope

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