## Algebra and Trigonometry 10th Edition

It seems that the area $A$ when $x=4$ is the maximum area.
$x~~~~~~~~~~~~~~~~A=4x-\frac{x^2}{2}$ $1~~~~~~~~~~~~~~4(1)-\frac{1^2}{2}=\frac{7}{2}$ $2~~~~~~~~~~~~~~4(2)-\frac{2^2}{2}=6$ $3~~~~~~~~~~~~~~4(3)-\frac{3^2}{2}=\frac{15}{2}$ $4~~~~~~~~~~~~~~4(4)-\frac{4^2}{2}=8$ $5~~~~~~~~~~~~~~4(5)-\frac{5^2}{2}=\frac{15}{2}$ $6~~~~~~~~~~~~~~4(6)-\frac{6^2}{2}=6$ $7~~~~~~~~~~~~~~4(7)-\frac{7^2}{2}=\frac{7}{2}$