9709 P13 - Jun 2020 - Q11
1269
The diagram shows part of the curve with equation \(y = x^3 - 2bx^2 + b^2x\) and the line \(OA\), where \(A\) is the maximum point on the curve. The \(x\)-coordinate of \(A\) is \(a\) and the curve has a minimum point at \((b, 0)\), where \(a\) and \(b\) are positive constants.
(a) Show that \(b = 3a\).
(b) Show that the area of the shaded region between the line and the curve is \(ka^4\), where \(k\) is a fraction to be found.
