Journal pg 215 #14, 21, 25, 28
s  16t 2  96t 112
14.
a.

v  32t  96
v(0)  96

b.


ft
sec
Maximum height occurs when
v 0
s  16t 2  96t 112
s(3)  256 ft
v  32t  96  0
t  3 sec

c.
Velocity when
s0

s  16t 2  96t 112  0
t 7, 1
21.
v  32t  96
v(7)  128


A  bh


 2x(4 cos(0.5x))
 8x cos(0.5x)
A 8x(0.5sin(0.5x))  8cos(0.5x)  0
x  1.7206672
Critical points:

1.72206672, 0, 1.7206672, 
Dimensions : 3.441X2.608 units
Area 8.977 units 2

25.
The sum of the length and girth cannot exceed 108 in.
V  LWH
L  108  4 x
W x
Hx
V  (108  4 x)x 2  108x 2  4 x 3

V  216x 12x 2  0
12x(18  x)  0
x  0, 18
Dimensions : L  108  4 x  36, H  18, W  18 in


V  11664 in 2
f (x)  x 2 
28.
a.
a
x
Find the value of a that would make the function have a local minimum at x = 2.
f (x)  2x  ax 2

 2x 
a 2x 3  a

0
x2
x2
2x 3  a  0
x 2
2(2) 3  a  0
a  16
b.

Find the value of a that would make the function have a point of inflection at x = 1.
f (x)
 

x 2 (6x 2 )  (2x 3  a)2x
x4
6x 4  4 x 4  2ax 2x 4  2ax

0
x4
x4
2x 4  2ax  0
2  2a  0
a  1

x 1