Chapter 2.2, Problem 34AYU

Cross-sectional Area The cross-sectional area of a beam cut from a log with radius 1 foot is given by the function $A\left(x\right)=4x\sqrt{1-x^2}$, where $x$ represents the length, in feet, of half the base of the beam. See the figure.

(a) Find the domain of A.

(b) Use a graphing utility to graph the function $A=A\left(x\right)$.

(c) Create a TABLE with $TblStart=0$ and $\Delta Tbl=0.1$ for $0\le x\le 1$. Which value of $x$ maximizes the cross-sectional area? What should be the length of the base of the beam to maximize the cross-sectional area?