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Getting Started 7
Take an 8½"×11" sheet of paper and cut X by X squares from two corners and X
by (X+B) rectangles from the other two corners. Now fold the paper into a box
with lid. What X would give the maximum volume V of a box made in this way?
Use tables and graphs to determine the solution.
Begin by defining a function that describes the
volume of the box.
From the diagram: 2X + A = W
2X + 2B = L
V = A B X
Substituting: V = (W – 2X) (L
à
2 – X) X
W
X
X
A
BXB
L
If necessary, press
z
†
Í
to change the
MODE
to
FLOAT
. Then press
y
.
‘
to
return to the Home screen and clear it.
1. Press
8.5
¿
ƒ
W
Í
to store the width of
the paper.
Press
11
¿
ƒ
L
Í
to store the length of
the paper.
2. You define functions for tables and graphs on the
Y=
edit screen.
Press
o
to access this screen.
3. Enter the function for volume as
Y1
. Press
£
ƒ
W
¹
2
@
¤
£
ƒ
L
¥
2
¹
@
¤
@
Í
to define function
Y1
in terms of
X
. (
@
lets you
enter
X
quickly without pressing
ƒ
.)
The
=
sign is highlighted to show that
Y1
is selected.
Defining a Function: Box with Lid