Posted by danny on Thursday, September 27, 2012 at 11:36pm.
An open box is made from a square piece of cardboard 20 inches on a side by cutting identical squares from the corners and turning up the sides.(a) Express the volume of the box, V , as a function of the length of the side of the square cut from each corner, x. (b) Find and interpret V (1),V (2),V (3),V (4), and V (5). What is happening to the volume of the box as the length of the side of the square cut increases? (c) Find the domain of V.

college algebra  Steve, Friday, September 28, 2012 at 11:18am
v = x(202x)^2
using what you know about the shape of cubic curves, clearly there is a maximum volume for 0 <= x <= 10 (this is also the domain of v)
Naturally, volume is zero when x=0 and when x=10.
A little checking of values will show that v(x) is max when x = 10/3.
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