An open box of maximum volume is made from a square piece of material 24centimeters 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?

Transcribed Image Text:

24 - 2x. X + 24 - 2x + X 1| 2 3 | 4 5 6 484 | 800 Volume, V Height, a 972 1024 | 980 864