1. The document describes a math practical experiment to find the length x that maximizes the volume of a box formed by cutting squares of length x from the corners of a rectangular cardboard sheet with length 4 units and width 6 units. 2. Using the Geogebra applet "box folding for maximum volume", students are instructed to observe how the box is formed by moving sliders and record the volume and slope of the tangent for different x values. 3. By analyzing the slope of the tangent, students can determine where the function is increasing or decreasing and find the local maxima, which is the maximum volume.

1. Math practical-1
Class 12

2. Experiment no. 1
• Aim: A rectangular piece cardboard
with length 4 units and width 6
units is given. A square of length x
units is cut from each corner and
the flaps are folded up to form an
open box. To find the length x to
maximize the volume of the box.
• Software requirements: Geogebra.
• Other requirements: print out of
the graph in the applet, external
usb memory
6 units
x
4units
4-2x
x
6-2x

3. Method followed
1. Open the applet “box folding for maximum volume”
and save it in the external memory with your name as
“Name_box folding for maximum volume” .
2. Work on this file now
3. Move the green slider of open/close box and observe
how the box is formed. Observe the volume of the box
while moving only the green slider.
Observation:
4. The blue and the red slider are for the length and
width of the sheet and the purple slider is for the height
of the box which is same as the square of side x that is
cut from the four corners of the sheet.
5. Move the slider h and record your observations for 5
different values x and of volume V.
6. For these values, record the values of the slope of the
tangent.
7. Find the values of x for which the function is
increasing and decreasing. Observe the nature of the
slope of tangent i.e. f’(x) in this interval.
8. Find the point of local maxima. What is the value of
f’(x) at this point?

4. Length = 4 units, width = 6 units
S. No. x Volume Point on the curve Slope of the tangent
1
2
3
4
5
Table 1
Observation 2.
1. The function is increasing for ____ and the slope of
tangent to the curve here is _____
2. The function is decreasing for ______ and the
slope of tangent to the curve here is _____
3. The local maxima is __________ and the maximum
volume is _______
4. The slope of tangent to the curve at the point of
local maxima is _____
Table 2
Observation 2.
1. The function is increasing for ____ and the slope of
tangent to the curve here is _____
2. The function is decreasing for ______ and the
slope of tangent to the curve here is _____
3. The local maxima is __________ and the maximum
volume is _______
4. The slope of tangent to the curve at the point of
local maxima is _____
Observations
Table 1
Observation 1
Length = units, width = units
S. No. x Volume Point on the curve Slope of the tangent
1
2
3
4
5
Table 2
Observation 1

5. Precautions
1. Copy the file in an external memory
and work on that file, don’t save your
work on the desktop file.
2. Don’t tamper with the in build
functions of the applet ; rather use a
fresh file to make a new applet if
needed.
3. Save the file with a different name in
the external memory, don’t overwrite
on the desktop file.
4. While taking a print out of the graph
applet, change the author’s name to
your own name.
Note : you may download geogebra classic from
https://www.geogebra.org/download