2026 TKGS WA2 Q3

Secondary 4

4 marks

The function \(f\) is given by \(f(x)=\dfrac{e^{-x}}{x^2+1}\). Explain with mathematical working, why \(f(x)\) is a decreasing function, for all real values of \(x\) and \(x\ne-1\).[4]

Solution:

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Answer:\(f'(x)=-\dfrac{e^{-x}(x+1)^2}{(x^2+1)^2}<0\) for \(x\ne-1\).

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