The image below will be needed to find the volume function
From the image above, we can see that the dimensions of the open box are
[tex](24-2x)\times x\times(24-2x)[/tex]Therefore, the volume function V is given as
[tex]V(x)=(24-2x)\times x\times(24-2x)[/tex]Thus,
[tex]\begin{gathered} V(x)=x(4x^2-96x+576) \\ V(x)=4x^3-96x^2+576x \end{gathered}[/tex]The volume function V is given by V(x) = 4x³ - 96x² + 576x
The domain of V is the values of x for which V is defined for this problem.
