Maximum Volume You construct an open box from a square piece of material, 36 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure). (a) Write a function V that represents the volume of the box. (b) Determine the domain of the function V . (c) Use a graphing utility to construct a table that shows the box heights x and the corresponding volumes V ( x ) . Use the table to estimate the dimensions that produce a maximum volume. (d) Use the graphing utility to graph V and use the graph to estimate the value of x for which V ( x ) is a maximum. Compare your result with that of part (c).
Maximum Volume You construct an open box from a square piece of material, 36 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure). (a) Write a function V that represents the volume of the box. (b) Determine the domain of the function V . (c) Use a graphing utility to construct a table that shows the box heights x and the corresponding volumes V ( x ) . Use the table to estimate the dimensions that produce a maximum volume. (d) Use the graphing utility to graph V and use the graph to estimate the value of x for which V ( x ) is a maximum. Compare your result with that of part (c).
Solution Summary: The author explains the function V that represents the volume of the box, made from a square piece of material, 36 inches, by cutting equal squares with sides of length x from the corners.
Maximum Volume You construct an open box from a square piece of material,
36
inches on a side, by cutting equal squares with sides of length
x
from the corners and turning up the sides (see figure).
(a) Write a function
V
that represents the volume of the box.
(b) Determine the domain of the function
V
.
(c) Use a graphing utility to construct a table that shows the box heights
x
and the corresponding volumes
V
(
x
)
. Use the table to estimate the dimensions that produce a maximum volume.
(d) Use the graphing utility to graph
V
and use the graph to estimate the value of
x
for which
V
(
x
)
is a maximum. Compare your result with that of part (c).
14
14
4. The graph shows the printing rate of Printer A. Printer B can
print at a rate of 25 pages per minute. How does the printing
rate for Printer B compare to the printing rate for Printer A?
The printing rate for Printer B is
than the rate
for Printer A because the rate of 25 pages per minute
is
than the rate of
for Printer A.
pages per minute
RIJOUT
40
fy
Printer Rat
Number of Pages
8N WA
10
30
20
Printer A
0
0
246
Time (min)
X
OR
16 f(x) =
Ef 16
χ
по
x²-2 410 | y = (x+2) + 4
Y-INT: y = 0
X-INT: X=0
VA: x=2
OA: y=x+2
0
X-INT: X=-2
X-INT: y = 2
VA
0
2
whole.
2-2
4
y - (x+2) = 27-270
+
xxx> 2
क्
above OA
(x+2) OA
x-2/x²+0x+0
2
x-2x
2x+O
2x-4
4
X<-1000 4/4/2<0 below Of
y
VA
X=2
X-2
OA
y=x+2
-2
2
(0,0)
2
χ
I need help solving the equation
3x+5=8
Chapter 3 Solutions
Bundle: College Algebra, Loose-leaf Version, 10th + WebAssign Printed Access Card for Larson's College Algebra, 10th Edition, Single-Term
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