Exercise. Let $f$ be given by

$f(x)=\{\begin{array}{ccc}4-x^2& if& x>0\\ 4-\frac{x^2}{4}& if& x0\end{array}$

The figure shows a rectangle with its sides parallel to the coordinate axes with two of its vertices on the curve $y=f(x)$ and above the $x-$axis and the other two vertices on the $x-$axis. Let the bottom right vertex be at the point $(x,0)$ for $xA(x)=,00.$

The area $of$ this rectangle $as$ a function $ofxis$

$A(x)=,0$