The graphs of $y=\mathrm{f}'\left( x \right)$ and $y=\left| \mathrm{f}\left( x \right) \right|$

Question

The graphs of $y=\mathrm{f}'\left( x \right)$ and $y=\left| \mathrm{f}\left( x \right) \right|$ are shown below. State the nature of all stationary points of the graph of $y=\mathrm{f}\left( x \right)$.[2] State the range of values of $x$ where $\operatorname{f}$ is decreasing,[2] $\mathrm{f}$ is concave upwards.[1] Sketch the graph of $y=\mathrm{f}\left( x \right)$ indicating clearly the asymptotes, coordinates of the stationary points and the intersections with the axes.[3]

Accepted Answer

(i) $(0,-1)$ is a minimum point, $(3,-3)$ is a maximum point (ii)(a) $x\leq0$ or $x\geq3$ (ii)(b) $-1<x<2$ (iii) The sketch has asymptotes $y=0$ and $x=2$, stationary points $(0,-1)$ and $(3,-3)$, $x$-intercept $(1,0)$, and $y$-intercept $(0,-1)$

2021 DHS Promo Q7

2021 DHS Promo Q7

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