Chapter 3 - Polynomial and Rational Functions - 3.4 Polynomial Functions: Graphs, Applications, and Models - 3.4 Exercises - Page 355: 94

$x=1.732$

Step 1. Use the figure given in the exercise, with $C(x,y)$ on the curve, we have $y=9-x^2$ Step 2. The area is given by $A=2xy=2x(9-x^2)=-2x^3+18x$ Step 3. Graph the above function as shown in the figure. Step 4. We can identify a local maximum for the area at $x=1.732$