2026 GESS P1 Q4

2026 GESS P1 Q4

Secondary 4
9 marks

The function \(f\) is defined, for all real values of \(x\), by \(f(x)=(x-2)x^2\).

  1. Find the values of \(x\) for which \(f\) is an increasing function.[3]
  2. Find the coordinates of the stationary points of \(f\) and determine the nature of these stationary points.[6]

Solution:

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Answer:(a) \(x<0\) or \(x>\dfrac43\). (b) Maximum \((0,0)\); minimum \(\left(\dfrac43,-\dfrac{32}{27}\right)\).

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