Chapter 4.4, Problem 56ES

In the context of Exercise 55, suppose that $0<A<B$ and the plywood sheet is $B$ feet tall, while the sheet is raised so that the horizontal distance between the bottom of the plywood and the platform edge is kept at $A$ feet. If the distance along the plywood from its bottom to the platform edge measures $x$ feet, then the top of the plywood will be $y=\left(\frac{B}{x}-1\right)\sqrt{x^2-A^2}\text{ feet}$ above the platform $\left(A\le x\le B\right)$ . What is the greatest distance above the platform that the top of the plywood reaches?