Given:
The expression for the volume of box in terms of x is,
[tex]4x^3-28x^2+144x[/tex]
Explanation:
The volume of cube is 1008. So equation for x is,
[tex]\begin{gathered} 4x^3-28x^2+144x=1008 \\ 4x^3-28x^2+144x-1008=0 \end{gathered}[/tex]
To determine the value of x, plot the equation on the graph.
Since the root of the equation is 7 and two remaining roots are imaginary. So possible value of x is 7, as height can never be imaginary value.
So box is 7 inches tall.
Answer: 7 inches
