2024 GESS PRELIMS P2 Q8
2024 GESS PRELIMS P2 Q8
6 marks
The equation of a curve is \(y = \frac{x}{e^{2x}}\).
- Find an expression for \(\frac{\mathrm{d}y}{\mathrm{d}x}\).[2]
- Given that \(x\) is changing at a constant rate of \(0.18\) units per second, find the rate of change of \(y\) when \(x = 1\).[2]
- Explain if the curve has more than one stationary point.[2]
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Answer:(a) \(\frac{\mathrm dy}{\mathrm dx}=\frac{1-2x}{e^{2x}}\) (b) \(\frac{\mathrm dy}{\mathrm dt}=-0.0244\text{ units/s}\) (3 s.f.) (c) Exactly one stationary point, at \(x=\frac12\)
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