■ No GDC ■ The diagram below shows two circles each with a radius of one unit. One circle is fixed with its centre at the origin \(\left( {0,\,0} \right)\). The other circle has its centre at the point B\(\left( {b,\,0} \right)\) such that \(0 \le b \le 2,\;b \in \mathbb{R}\). Changing the value of \(b\) causes the circle with centre B to move along the x-axis and for the area of the region where the circles overlap to increase or decrease accordingly. Let \(A\left( b \right)\) be a function...