Solutions to Some Practice Problems for the 1A Final
These are just answers so you can check that you did the problem correctly. For full credit
on an exam you would need to show all your work.
1.
x
= 1000 ft,
y
= 1500 ft, make sure you check that this gives an ABSOLUTE minimum,
and not just a local min.
2.
4000 cm
3
, again make sure this is an absolute max.
3.
(1
,
3), verify that it is the absolute min.
4.
x
= 500,
y
= 125, check that this makes the product an absolute max.
5.
V
=
πr
2
h
+
2
3
πr
3
, and we want to minimize surface area which is
SA
=
πr
2
+2
πrh
+2
πr
2
,
the answer is when
r
=
(
3
V
5
π
)
1
/
3
, and then solve for what
h
is also. You also need to check
that this is an absolute minimum.
6.
R
(
x
) =
xp
(
x
) where
p
(
x
) =

0
.
001
x
+ 23, for 0
≤
x
≤
15000 and
R
(
x
) is at an absolute
maximum when
x
= 11500, so the price is
p
(11500) = $11.50
7.
x
3
=
4
5
8.
1
.
895494
9.
Find
f
for the following
(a)
f
=
1
2
x
2
+
25
9
·
14
x
14
/
5
+
Cx
+
D
(b)
f
=
t
5
+
1
2
Cx
2
+
Dx
+
E
(c)
f
= 3
x
3
/
2

2
x
1
/
2
+ 2
(d)
f
=
2
7
t
7
/
2
+
4
5
t
5
/
2
+
C
(e)
f
=
1
4
x
4

5 cos
x
+
C
10.
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 Fall '09
 Stankova
 Math, Trigraph, 1000 FT, sin t dt, $11.50 7

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