2026 IGCSE Additional Mathematics May/June 0606/11 Q7

A curve has equation \(y=\dfrac{4+e^{2x}}{2+e^x}\).

1. Show that, when \(\dfrac{\mathrm{d}y}{\mathrm{d}x}=0\), \(e^{2x}+4e^x-4=0\).[5]
2. Hence find the \(x\)-coordinate of the stationary point on the curve.
   Give your answer in the form \(\ln(a\sqrt b+c)\), where \(a\), \(b\) and \(c\) are integers.[4]