lecture15

# lecture15 - 3) Find the velocity when the ball hit the...

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Lecture 15 1 Lecture 15 (Sec. 3.5) Higher Order Derivatives ex. Let f ( x ) = 2 x 2 + 1 1) Find f 0 ( x ).

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Lecture 15 2 2) Find d dx [ f 0 ( x )]. NOTE: We write f 00 ( x ) =
Lecture 15 3 Higher Order Derivatives For y = f ( x ), we can write 1) The ﬁrst derivative : f 0 ( x ) = dy dx = d dx [ f ( x )] 2) The second derivative : 3) The third derivative: n ) The n th derivative: NOTE:

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Lecture 15 4 ex. (A polynomial example) Find all higher order derivatives for f ( x ) = 2 x 4 - 5 x 2 + 3 x - 1
Lecture 15 5 Applications of the Second Derivative Velocity and Acceleration Recall the following ideas: Position Function s ( t ) NOTE: h ( t ) Average velocity : Instantaneous velocity(velocity function) :

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Lecture 15 6 Consider the following position function: The height (in feet above the ground) of an object which is free-falling, neglecting air resistance, is given by h ( t ) = where v 0 = and h 0 = ex. A person on a cliﬀ 160 feet above the ground threw a ball upward with an initial velocity of 48 feet per second. 1) Find a formula for h ( t ), which gives the ball’s height above the ground t seconds after it is thrown.
Lecture 15 7 2) What was the maximum height the ball reached?

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Unformatted text preview: 3) Find the velocity when the ball hit the ground. Lecture 15 8 Acceleration ex. A ball is thrown upward from a cliﬀ 160 ft. above the ground with initial velocity of 48 feet per second. Find its acceleration at any time t . Lecture 15 9 ex. A particle moves along a path deﬁned by the position function s ( t ) = ( t 3 + 1) 1 3-1 where s ( t ) is the position (in inches from the starting point) of the particle after t seconds. Find a formula for the acceleration at any time t . Lecture 15 10 Application: Second Derivative and Rate of Change ex. Total sales S (in hundreds of dollars) of a prod-uct are related to the amount of money x spent on advertising according to the function S ( x ) =-. 002 x 3 + 0 . 6 x 2 + x + 500 where x is measured in thousands of dollars and ≤ x ≤ 200. Compute S (120) and S 00 (120) and interpret the results....
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## This note was uploaded on 07/18/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.

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lecture15 - 3) Find the velocity when the ball hit the...

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