The diagram below shows the curve $y=\mathrm{f}'(x)$ which passes through $(-3,0)$ and has turni

Question

The diagram below shows the curve $y=\mathrm{f}'(x)$ which passes through $(-3,0)$ and has turning points at $(2,0)$ and $\left(8,\dfrac{2}{3}\right)$. The lines $x=0$ and $x=4$ are the asymptotes of the curve. State the range of values of $x$ such that the curve $y=\mathrm{f}(x)$ is concave upwards.[2] State the $x$-coordinates of the stationary points for the curve $y=\mathrm{f}(x)$ and determine the nature of these stationary points.[3] Line $L$ is the normal to the curve $y=\mathrm{f}(x)$ at the point $(8,10)$. Find the equation of $L$.[2]

Accepted Answer

(i) $x8$ (ii) $x=-3$: minimum point; $x=2$: stationary point of inflexion (iii) $y=-\dfrac{3}{2}x+22$

2026 NJC Promo Q5

2026 NJC Promo Q5

Solution:

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