Since the range of the function is 0 to 7.5, the first column begins with the minimum value and continuing through the maximum value with an interval of .5.

The maximum value (when X is approx. 3) is about 513 cubic inches. The box has a volume of 400 cubic inches when the height is about 1.525 inches cubed and 4.79 inches cubed.

 

 

Finally, using the ideas and consistent approximations the maximum value can be determined using calculus by taking the derivative of the function.