{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

calc notes lecture 11

# calc notes lecture 11 - 4 3 2 f x x x = 1 Example 2 Find...

This preview shows pages 1–4. Sign up to view the full content.

Lecture Sections Objectives Assignment 11 2.6 Higher-Order Derivatives 2.6: 1-39 eoo. 43, 47, 51-57 Understanding Goals: 1. To understand the definition of higher-order derivatives. 2. To understand how to use the position functions to determine the velocity and acceleration of moving objects. Notation for Higher-Order Derivatives First derivative: ', y '( ), f x dy dx , [ ] ( ) d f x dx , [ ] x D y Second derivative: ", y "( ), f x 2 2 d y dx , [ ] 2 2 ( ) d f x dx , [ ] 2 x D y Third derivative: '", y '"( ), f x 3 3 d y dx , [ ] 3 3 ( ) d f x dx , [ ] 3 x D y Fourth derivative: (4) , y (4) ( ), f x 4 4 d y dx , [ ] 4 4 ( ) d f x dx , [ ] 4 x D y . . . nth derivative: ( ) , n y ( ) ( ), n f x n n d y dx , [ ] ( ) n n d f x dx , [ ] n x D y The n th-order derivative of an n th-degree polynomial function 1 1 1 0 ( ) n n n n f x a x a x a x a - - = + + + + ��� is the constant function ( ) ( ) ! n n f x n a = . Each derivative of order higher than n is the zero function. Example 1 : Find the fourth derivative of

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 4 3 ( ) 2 f x x x =-. 1 Example 2 : Find the value of (4) (2) f if 1 ( ) f x x = . 2 differentiate differentiate Position function ( ) Velocity function ( ) Acceleration function ( ) s t v t a t ( ) s t ( ) ds v t dt = 2 2 '( ) ( ) d s v t a t dt = = Example 3 : A ball is thrown into the air from the top of a 160-foot cliff. The initial velocity of the ball is 48 feet per second, which implies that the position function is 2 16 48 160 s t t = -+ + where the time t is measured in seconds. Find the height, the velocity, and the acceleration of the ball when 3. t = 3 Example 4 : Find the second order derivative of ( 29 2 | 4 | f x x =-. 4...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern