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