Maximum Volume An open box of maximum volume is made from a square piece of material 24 centimeters on a side by cutting equal squares from the corners and turning up the sides (see figure). (a) The table shows the volumes V (in cubic centimeters) of the box for various heights x (in centimeters). Use the table to estimate the maximum volume. (b) Plot the points ( x , V ) from the table in part (a). Does the relation defined by the ordered pairs represent V as a function of x ? (c) Given that V is a function of x , write the function and determine its domain.
Maximum Volume An open box of maximum volume is made from a square piece of material 24 centimeters on a side by cutting equal squares from the corners and turning up the sides (see figure). (a) The table shows the volumes V (in cubic centimeters) of the box for various heights x (in centimeters). Use the table to estimate the maximum volume. (b) Plot the points ( x , V ) from the table in part (a). Does the relation defined by the ordered pairs represent V as a function of x ? (c) Given that V is a function of x , write the function and determine its domain.
Solution Summary: The author explains how to determine the maximum volume of a square box for various heights using the table given below.
Maximum Volume An open box of maximum volume is made from a square piece of material
24
centimeters on a side by cutting equal squares from the corners and turning up the sides (see figure).
(a) The table shows the volumes
V
(in cubic centimeters) of the box for various heights
x
(in centimeters). Use the table to estimate the maximum volume.
(b) Plot the points
(
x
,
V
)
from the table in part (a). Does the relation defined by the ordered pairs represent
V
as a function of
x
?
(c) Given that
V
is a function of
x
, write the function and determine its domain.
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY