1) An open-top box is to be constructed from a 6 foot by 8 foot rectangular cardboard by cutting out equal sq

Question

1) An open-top box is to be constructed from a 6 foot 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.
a) Find the function V that represents the volume of the box in terms of x.




b) Graph this function and show the graph over the valid range of the variable x..





c) Using the graph, what is the value of x that will produce the maximum volume?

Answer 1

a) V=lwh
V(x)=(8-2x)(6-2x)x or V(x)=4x^3-28x^2+48x

b) Do this on a graphing calculator. The valid range will be from 0 to approximately 24.258. Range [0, 24.258] The domain for this problem would be from x=0 to x=3. [0,3] When you graph it use this window [0,3] [0,25].

c) The x that will produce the max volume is the x part of the vertex, approximately 1.131 feet.