Chapter 4.4, Problem 55ES

At a construction site, a worker raises an $8\text{-foot}$ sheet of plywood to a platform by sliding the sheet up over the edge of the platform in such a way that the horizontal distance between the bottom of the plywood and the platform edge is kept at $1$ foot. If the distance along the plywood from its bottom to the platform edge measures $x$ feet, then the top of the plywood will be $y=\left(\frac{8}{x}-1\right)\sqrt{x^2-1}\text{ feet}$ Above the platform $\left(1\le x\le 8\right)$ . What is the greatest distance above the platform that the top of the plywood reaches?