Chapter 3 Section 05

Chapter 3 Section 05 - 1 Chapter 3 Section 05 Higher Order...

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Unformatted text preview: 1 Chapter 3 Section 05 Higher Order Derivatives page 162 2 Objectives 1. Find 2 nd and 3 rd derivatives. 2. Interpret 2 nd and 3 rd derivatives of functions. 3. Find a formula for the nth derivative of a function. 4. Work distance, velocity, acceleration applications. 3 Higher derivatives Since the derivative of f is a function, it may also have a derivative. If so, it is called the 2 nd derivative of f. )] ( [ ) ( 4 )] ( [ ' ' ' ) ( ' ' ' 3 )] ( [ ' ' ) ( ' ' 2 4 4 4 ) 4 ( ) 4 ( 3 3 3 2 2 2 x f D dx y d y x f derivative th x f D dx y d y x f derivative rd x f D dx y d y x f derivative nd = = = = = = = = = 4 Example: f(t) = t 4 7t 2 + 2 f(t) = 4t 3 14t f(t) = 12t 2 14 f(t) = 24t f (4) = 24 f (5) = 0 f (6) = 0 Etc. f (n) = 0 For any polynomial, f (n) = 0 for n degree + 1 5 4 2 2 2 2 2 2 2 ) 1 ( ) 2 2 )( 2 ( ) 2 2 ( ) 1 ( ' ' ) 1 ( 2 ' ) 1 ( ) 1 ( 2 ) 1 ( ' 1 of derivative second the Find + + +- + + = + + = + - + = + = x x x x x x y x x x y x x x x y x x y 6...
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This note was uploaded on 09/28/2009 for the course MATH 1550 taught by Professor Wei during the Spring '08 term at LSU.

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Chapter 3 Section 05 - 1 Chapter 3 Section 05 Higher Order...

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