June 2025 Paper 1 Q2

OCR ACurrent spec4 marksDifferentiationSketching & Transforming Graphs

2

Sketch of an n-shaped curve through the origin O, crossing the positive x-axis, with a maximum point above the positive x-axis

The diagram shows the curve \(y = ax(x-b)\), where \(a\) and \(b\) are constants and \(b \gt 0\).

(a) Given that the curve has a stationary point at \(x = 3\), state the value of \(b\). [1]
(b) Given also that the stationary point at \(x = 3\) is a maximum, state what can be deduced about the value of \(a\). [1]
(c) Find the \(y\)-coordinate of the stationary point, giving your answer in terms of \(a\). [1]
(d) State the range of values of \(x\) for which the curve is increasing. [1]
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