Consider the function \(f\) given by

\[ f(x) = \begin{cases} 4-x^2, & \text { if } x>0\\ 4-\frac {x^2}{4}, & \text { if } x\leq 0 \end{cases}. \]
Consider a rectangle with sides parallel to the axes, having two vertices on the \(x\)-axis, and the other two vertices on the graph of \(f\) above the \(x\)-axis.

The area of the rectangle as a function of \(l\) is (see picture above)

\[ A(l) = \answer {3l(4-l^2)}. \]
The domain of the function \(A\) is \(\left [\answer {0},\answer {2}\right ]\).

The width of the rectangle with the maximum area is \(\answer {2\sqrt {3}}\) and its height is \(\answer {\frac {8}{3}}\).