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

Question

The equation of a curve is $y=\frac{\ln 2x}{x}$ Find an expression for $\frac{\mathrm{d}^2y}{\mathrm{d}x^2}$ and show that $x\frac{\mathrm{d}^2y}{\mathrm{d}x^2}+2\frac{\mathrm{d}y}{\mathrm{d}x}+\frac{1}{x^2}=0$[5] Find the exact coordinates of the stationary point of the curve and use the second derivative test to determine if the stationary point is a maximum or minimum.[5]

Accepted Answer

(i)$\frac{\mathrm{d}^2y}{\mathrm{d}x^2}=\frac{2\ln {2x}-3}{x^3}$ (ii)stationary point : $ \left(\frac{\mathrm{e}}{2},2\mathrm{e}^{-1} \right)$, maximum point

2025 CHS PRELIMS P2 Q7

2025 CHS PRELIMS P2 Q7