2025 IGCSE 0580 May/June P22 Q21

2025 IGCSE 0580 May/June P22 Q21

9 marks

The diagram shows the graph of \(y=3x-x^3\).

The graph crosses the \(x\)-axis at \(A\), at \(O\) and at \(B\).

The turning points of the graph are at \(P\) and at \(Q\).

  1. Find the \(x\)-coordinate of \(A\) and the \(x\)-coordinate of \(B\).
    Give your answers as exact values.[3]
    1. Differentiate \(3x-x^3\).[2]
    2. Find the coordinates of \(P\) and \(Q\).[4]

Solution:

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Answer:(a) \(x_A=-\sqrt3,\ x_B=\sqrt3\). (b)(i) \(3-3x^2\). (ii) \(P=(-1,-2),\ Q=(1,2)\).

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