SOLUTION: I am having a hard time doing this problem. An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the fol

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I am having a hard time doing this problem. An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the fol      Log On


   

Question 52399: I am having a hard time doing this problem.
An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out.
Find the function V that represents the volume of the box in terms of x.
Graph this function and show the graph over the valid range of the variable x.
Using the graph, what is the value of x that will produce the maximum volume?
For the function V that represents the volume of the box in terms of x.....I think the answer is: V=x(6-2x)(8-2x). But I'm not sure. And I don't know how to graph it.
Thanks for your time.
Answer by ChillyWiz(11) About Me  (Show Source):
You can put this solution on YOUR website!
The graph of this polynomial in fuctional notation and simplfied will be
V%28x%29=4x%5E3-14x%5E2%2B48x
Notice x>0 because it is impossible to have an 0 length in volume, and negative numbers are also clearly impossible
Plot in your graphing calcultor this function, where Y=4x%5E3-14x%5E2%2B48x
Your Window should look like
X(min)= -8.5 Y(min)= 0
X(max)= 27 Y(max)= 62
X(step/scl)= 6 Y(step/scl)= 6
You will see the maximum occurs when x=2.4