We have , that measure of the side of the square is x
Therefore
l=26-2x
w=20-2x
h=x
Therefore the Volume function is
[tex]V=(26-2x)(20-2x)x[/tex]
Then we simplify
[tex]V(x)=4x^3-92x^2+520x[/tex]
6.In the context of obtaining a Volume we can't have negative numbers for x and for the function by observing the graph
Domain
[tex]0\le x\le10[/tex]
Therefore for the range
[tex]0\: 7.
Because we have a polynomial
the domain without the constrain
[tex]-\infty\: the range without the constrain
[tex]-\infty\: 8.
Since the leading term of the polynomial is 4 x^{3}, the degree is 3, i.e. odd, and the leading coefficient is 4, i.e. positive. This means
[tex]\begin{gathered} x\to-\infty,\text{ }f(x)\to-\infty \\ x\to\infty,f(x)\to\infty \end{gathered}[/tex]
