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
You can always match 4 points using a cubic polynomial. A graphing calculator can find a cubic regression equation for you. This set of points is matched by .. y = x^3 +3x^2 +5x +3
