## Calculus: Early Transcendentals 8th Edition

$S(l)=l^{2} + \frac{8}{l}, l\gt0$
Let the height of the box be $h$ and the sides of the square base be length $l$. Volume = $h\times l\times l=2$ $h=\frac{2}{l^{2}}$ Surface Area = Area of base + Area of 4 other sides = $l\times l + 4(l\times h)$ = $l^{2} + \frac{8}{l}$ $\because$ All lengths are positive, $l\gt0$ $h=\frac{2}{l^{2}}\gt0$