A curve $C$ has equation $y=x^{-3}\ln x$. Show that \(\frac{\mathrm{d}y}{\mathrm{d}x}=\frac

Question

A curve $C$ has equation $y=x^{-3}\ln x$. Show that $\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{1-3\ln x}{x^4}$ and hence find the coordinates of the turning point of $C$.[4] Find the exact area enclosed by $C$, the $x$-axis and the line $x=3$.[5]

Accepted Answer

(a) $\left(\mathrm{e}^{1/3},\frac1{3\mathrm{e}}\right)$ (b) $\frac29-\frac{\ln3}{18}$

N2022 P1 Q7

N2022 P1 Q7

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