Given polynomial:
[tex]V(x)=1500x-x^2[/tex]Where x is the length of the fence in feet.
The maximum area of the enclosure can be found by differentiating the polynomial with respect to x and equating to zero.
We have:
[tex]\begin{gathered} V^{\prime}(x)\text{ = 1500 - 2x} \\ 1500\text{ - 2x = 0} \\ 2x\text{ = 1500} \\ \text{Divide both sides by 2} \\ \frac{2x}{2}\text{ = }\frac{1500}{2} \\ x\text{ = 750} \end{gathered}[/tex]Substituting the value of x back into the enclosure function:
[tex]\begin{gathered} V(x=750)\text{ = 1500 }\times750-(750)^2 \\ =\text{ 562500} \end{gathered}[/tex]Answer:
562500
