2026 GESS P1 Q2

2026 GESS P1 Q2

Secondary 4
6 marks

The curve \(y=f(x)\) is such that \(f'(x)=e^x+e^{-2x}\).

  1. Explain why the curve \(y=f(x)\) has no stationary points.[2]
  2. Given that the curve passes through the point \(\left(0,\dfrac32\right)\), find an expression for \(f(x)\).[4]

Solution:

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Answer:(a) \(f'(x)>0\) for all real \(x\). (b) \(f(x)=e^x-\dfrac12e^{-2x}+1\).

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