2022 BTYSS P1 Q10

2022 BTYSS P1 Q10

Secondary 4
7 marks
  1. Differentiate \(\dfrac6{(x^2+1)^2}\) with respect to \(x\).[2]
  2. Hence evaluate \(\displaystyle\int_{-1}^2\dfrac{12x}{(x^2+1)^3}\,\mathrm dx\).[3]
  3. Explain why the curve \(y=\dfrac6{(x^2+1)^2}\) is a decreasing function for \(x>0\).[2]

Solution:

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Answer:(a) \(-\dfrac{24x}{(x^2+1)^3}\). (b) \(\dfrac{63}{100}\). (c) Derivative negative for \(x>0\).

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