The equation of a curve is $y = \frac{x}{e^{2x}}$. Find an expression for \(\frac{\mathrm{d}y

Question

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]

Accepted Answer

(a) $ \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{1 - 2x}{\mathrm{e}^{2x}} $ (b) $-0.0244$ units/sec

2024 GESS PRELIMS P2 Q8

2024 GESS PRELIMS P2 Q8