13112an4.4-7

13112an4.4-7 - c Kendra Kilmer February 28, 2012 Section...

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c c Kendra Kilmer February 28, 2012 Section 4.3 - Derivatives and the Shapes of Curves Increasing/Decreasing Test: If f ( x ) > 0 on an interval, then f is on that interval. If f ( x ) < 0 on an interval, then f is on that interval. The First Derivative Test Suppose that x = c is a critical number of a continuous function f . 1. If f ( x ) changes from to at x = c , then we have that f ( x ) is and at x = c there is a . 2. If f ( x ) changes from to at x = c , then we have that f ( x ) is and at x = c there is a . 3. If the sign of f ( x ) is the same on both sides of x = c , then at x = c . Example 1: Determine the intervals where the following functions are increasing and decreasing and find the local extrema. a) f ( x ) = ( x + 2 ) e x b) g ( x ) = x 4 + 2 x 3 + 5 c) h ( x ) = x + 3 5 x 4
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c c Kendra Kilmer February 28, 2012 Second Derivative Test for Local Extrema: Let c be a critical value for f ( x ) .
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13112an4.4-7 - c Kendra Kilmer February 28, 2012 Section...

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