SOLUTION: 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 e

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 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 e      Log On


   

Question 33298: 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
Using the graph, what is the value of x that will produce the maximum volume?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Starting with the formula for the volume of a rectangular prism (a box):
V+=+L%2AW%2Ah The height of the box will be just x. The length, after cutting an x-square from each corner, will be 8-2x and the width will be 6-2x.
Now we can write the function (V) of the volume in terms of x.
V+=+%288-2x%29%286-2x%29x Simplify.
V+=+4x%5E3+-+28x%5E2+%2B+48x This is the required function.
The graph is:
graph%28300%2C200%2C-5%2C5%2C-10%2C30%2C4x%5E3-28x%5E2%2B48x%29
By inspection, the maximum volume occurs at approximately x = 1