Solving a word problem by finding a local extremum of a polynomial function
A box with a hinged lid is to be made out of a rectangular piece of cardboard that measures
inches by
inches. Six squares will be cut from the cardboard: one square will be cut from
each of the corners, and one square will be cut from the middle of each of the
inch sides
(see Figure 1). The remaining cardboard will be folded to form the box and its lid (see Figure
2). Letting
represent the sidelengths (in inches) of the squares, use the
ALEKS graphing
calculator
to find the value of
that maximizes the
volume
enclosed by this box. Then give
the maximum volume. Round your responses to two decimal places.
After cutting
squares of side length
from a side with length
, the cardboard remaining on
this side will have length
. Thus, the
pieces
of cardboard left will each have length
.
Furthermore, cutting
squares of side length
from a side with length
yields a piece of
cardboard with length
(see Figure 3).
Therefore, the box formed from this cut rectangle will have
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Self
 Rectangle, maximum volume, ALEKS graphing

Click to edit the document details