Unformatted text preview: the derivative of the Cost function.
1. A particle moves along a line so that its position at any time t ≥ 0 is given by s HtL = t2  t  4,
measured in meters and t is measured in seconds. Find HaL the displacement in the first 3 seconds
HbL the average velocity in the first 3 seconds
HcL the acceleration at t = 3 seconds
HdL where the particle is when s is a minimum
HeL the velocity when t = 3 seconds
HaL s H3L  s H0L = 2  H 4L where s is 6 meters
m
HbL average velocity = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄÄÄ
ÄÄÄÄÄÄÄÄ Ä
= 2 ÄÄÄÄÄÄÄÄÄÄÄÄÄ
Ä
3 seconds
sec
m
HcL v HtL = 2 t  1
a HtL = 2
a H3L = 2 ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
Ä
sec2
1
HdL find where the derivative is 0
2t  1 = 0
t = ÄÄÄÄÄ second, and check the endpoints so
2
1
i1y
jz
s H0L =  4 meters
s H1L =  4 meters
s j ÄÄÄÄÄ z =  4 ÄÄÄÄÄ m...
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This note was uploaded on 02/11/2013 for the course MATH 1 taught by Professor Greene during the Spring '08 term at UCLA.
 Spring '08
 GREENE
 Calculus, Rate Of Change

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