Given:
Find-:
The maximum possible volume of this box
Explanation-:
For maximum possible volume,
So, volume is:
[tex]V(x)=x(14-2x)(11-2x)[/tex]
For maximum volume:
[tex]\begin{gathered} V(x)=x(154-28x-22x+4x^2) \\ \\ V(x)=x(4x^2-50x+154) \\ \\ V(x)=4x^3-50x^2+154x \end{gathered}[/tex]
Graph of function:
Maximum is:
[tex](x,f(x))=(2.039,14.039)[/tex]
So the maximum possible volume is 14.039
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