calculus (PRE)
posted by Ty on .
This may be simple, but I'm not getting it. An open box of maximum volume is to be made from a square piece of material, 24cm on a side, by cutting equal squares from the corners and turning up the sides. The table for it is:
Height(x) Volume(V)
1 484
2 800
3 972
4 1024
5 960
6 864
If volume,V, is a function of x write the function and its domain.

The table should be:
1, 484
2, 800
3, 972
4, 1024
5, 960
6, 864
Sorry! 
volume= x^3 domain is 0<x<24cm

height x
length = 24  2x
width = 24  2x
volume = x(242x)(242x)
v = x(576  96 x + 4 x^2)
v = 4 x^3 96 x^2 + 576 x
now x may not be negative
x may not be equal to or greater than 12 or there is no box bottom left
so
0 < x <12