A box with a lid is to be made from a rectangular piece of cardboard 15 cm by 17 cm, as shown in the figure below. Two equal squares of side $\displaystyle {x}$ are to be removed from one end, and two equal rectangles are to be removed from the other end so that the tabs can be folded to form the box with a lid. Find $\displaystyle {x}$ such that the volume of the box is a maximum.

The equation that gives the volume of the box in terms of the length of $\displaystyle {x}$ is: $\displaystyle {V}={x}{\left({8.5}-{x}\right)}{\left({15}-{2}{x}\right)}$



What is the domain of the function in context of the problem? $\displaystyle ≤{x}≤$

Length of the equal squares that are removed: $\displaystyle {x}=$ Select an answer cm^3 cm^2 cm .
Volume of the box: $\displaystyle {V}=$ Select an answer cm^3 cm cm^2 .