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0580 P22 - Jun 2025 - Q21 - 9 marks
10952

The graph of \(y=3x-x^3\) crosses the x-axis at A, O and B. Its turning points are P and Q.

Sketch of negative cubic with intercepts A O B and turning points P Q

(a) Find the exact x-coordinates of A and B. [3]

(b(i)) Differentiate \(3x-x^3\). [2]

(b(ii)) Find P and Q. [4]

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