14209an5.1-6

14209an5.1-6 - c circlecopyrt Kendra Kilmer March 8 2009...

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Unformatted text preview: c circlecopyrt Kendra Kilmer March 8, 2009 Section 5.1 - First Derivative and Graphs Example 1: x y f(x) 2 4 6 8 10-2-4-6-10 -8-2-4-6-8-10 2 4 6 8 10 Conclusions: 1 c circlecopyrt Kendra Kilmer March 8, 2009 We will be creating sign charts of f ′ ( x ) to determine important information about f ( x ) . Definition: A partition number of f ′ ( x ) is a value of x such that • • Definition: A critical value of f ( x ) is a value of x such that • • • Example 2: Find the critical values and partition numbers for the following functions and then con- struct a sign chart for the first derivative to determine where the function is increasing/decreasing. a) f ( x ) = − x 3 + 12 x − 5 2 c circlecopyrt Kendra Kilmer March 8, 2009 b) g ( x ) = x + 3 5 − x c) h ( x ) = x ln x − x 3 c circlecopyrt Kendra Kilmer March 8, 2009 Example 3: Let’s discuss the idea of local extrema: x a b c d e f(x) Definitions: • We call f ( c ) a local maximum if there exists an interval ( m , n )...
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This note was uploaded on 03/27/2012 for the course MATH 142 taught by Professor Drost during the Fall '08 term at Texas A&M.

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14209an5.1-6 - c circlecopyrt Kendra Kilmer March 8 2009...

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