The diagram below shows the graph of $y=\mathrm{f}'(x)$, the derivative graph of \(y=\mathrm{f}(x)

Question

The diagram below shows the graph of $y=\mathrm{f}'(x)$, the derivative graph of $y=\mathrm{f}(x)$. The graph has a horizontal asymptote at $y=1$, a minimum point at $(2,-1)$ and a point of inflexion at $(3,0)$. Using the graph above, state the range of values of $x$ for which the graph of $y=\mathrm{f}(x)$ is concave downwards.[1] state the value(s) of $x$ for the stationary points of $y=\mathrm{f}(x)$, determining the nature of each stationary point(s).[3] sketch $y=\mathrm{f}’’(x)$, , stating clearly the $x$-coordinate of the turning point(s) and the $x$-intercept(s).[3]

Accepted Answer

(i) $x<2$ (ii) $x=1$: maximum point; $x=3$: minimum point (iii) The graph of $y=\mathrm{f}''(x)$ has an $x$-intercept at $x=2$, a maximum turning point at $x=3$, and approaches $y=0$ from above as $x\to\infty$

ACJC Tutorial 11 Q1

ACJC Tutorial 11 Q1

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