Posted by **Ty** on Monday, November 21, 2011 at 5:53pm.

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.

- calculus (PRE) -
**Ty**, Monday, November 21, 2011 at 6:04pm
The table should be:

1, 484

2, 800

3, 972

4, 1024

5, 960

6, 864

Sorry!

- calculus (PRE) -
**bobpursley**, Monday, November 21, 2011 at 6:04pm
volume= x^3 domain is 0<x<24cm

- calculus (PRE) -
**Damon**, Monday, November 21, 2011 at 6:08pm
height x

length = 24 - 2x

width = 24 - 2x

volume = x(24-2x)(24-2x)

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

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