The volume of a crate with length of x feet, width of 8 - x feet, and a height of x - 3 feet is given by V(x)=x(8−x)(x−3) find the maximum volume of the crate and the dimensions for this volume
First, we need to find the maximum volume. In order to do this, we will first look at the dimensions of x and 8-x in the equation for volume. We can see that as x increases, so does 8-x. This means that there is a positive correlation between them. This also tells us that as x continues to increase, there will be a point where 8-x will equal 0. The maximum volume will occur when 8-x equals 0.
Therefore, the dimensions for the maximum volume are x=8 and x=-3.
Now we can solve for the actual maximum volume:
V max =(8)(8)-(3)(8)=64.
The maximum volume is 64 cubic feet and the dimensions for this volume are 8x=-3
