The diagram below shows the graph of $y=\mathrm{{f}'}\left( x \right)$intersecting the $x$-axis

Question

The diagram below shows the graph of $y=\mathrm{{f}'}\left( x \right)$intersecting the $x$-axis at $x=-3$ and $x=1$. Given that $\mathrm{f}\left( -3 \right)=4$ and $\mathrm{f}\left( 1 \right)=1$, state the coordinates of the stationary points and their nature of $y=\mathrm{f}\left( x \right)$,[3] find the range of values of $x$ for which the curve $y=\mathrm{f}\left( x \right)$ is strictly decreasing,[2] sketch the graph of $y=\mathrm{f}\left( x \right)$.[2]

Accepted Answer

(i) ${(1,1)}$ is a minimum point; ${(-3,4)}$ is a stationary point of inflexion (ii) ${x < -3}$ or ${-3 < x < 1}$

2010 TPJC P1 Q6

2010 TPJC P1 Q6

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