${y = \mathrm{f}(x)}$ ${y = \mathrm{f}'(x)}$ At $x=2$, $\mathrm{d}y/\mathrm{d}x=3/2$.

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Rows 1–3: see worked sketches. Zeros: (1) $x=2$; (2) $x=-1$, with central minimum $(2,\frac32)$; (3) $x=0,2$. Vertical asymptotes: $x=-2$; $x=0,4$; $x=1$, respectively. Horizontal asymptotes: $y=0,0,-1$, respectively.

Applications of Differentiation - Sketching Derivative Graphs

Applications of Differentiation - Sketching Derivative Graphs

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\({y = \mathrm{f}(x)}\)	\({y = \mathrm{f}'(x)}\)

At \(x=2\), \(\mathrm{d}y/\mathrm{d}x=3/2\).