This preview shows pages 1–6. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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...
View
Full
Document
This note was uploaded on 09/28/2009 for the course MATH 1550 taught by Professor Wei during the Spring '08 term at LSU.
 Spring '08
 Wei
 Calculus, Derivative

Click to edit the document details