2023 YTSS P2 Q5

2023 YTSS P2 Q5

Secondary 4
6 marks

The equation of a curve is \(y=\dfrac{6x^2}{2-5x}\) for \(x\ne\dfrac25\).

  1. Express \(\dfrac{\mathrm dy}{\mathrm dx}\) in the form \(\dfrac{ax(4-bx)}{(2-5x)^2}\), where \(a\) and \(b\) are integers to be determined.[3]
  2. State the range of values of \(x\) for which \(y\) is a decreasing function.[3]

Solution:

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Answer:(a) \(\dfrac{6x(4-5x)}{(2-5x)^2}\), \(a=6,b=5\). (b) \(x<0\) or \(x>\dfrac45\).

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