Question Number 147753 by Odhiambojr last updated on 23/Jul/21
$${Find}\:{a}\:{point}\:{on}\:{the}\:{curve} \\ $$$$\:{y}={x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{3}\:{at}\:{which}\:{the}\:{tangent}\:{is} \\ $$$$\:{parallel}\:{to}\:{the}\:{x}-{axis} \\ $$
Answered by Olaf_Thorendsen last updated on 23/Jul/21
$$\frac{{dy}}{{dx}}\:=\:\mathrm{2}{x}−\mathrm{2}\:=\:\mathrm{2}\left({x}−\mathrm{1}\right) \\ $$$$\frac{{dy}}{{dx}}\:=\:\mathrm{0}\:\:\Leftrightarrow\:{x}\:=\:\mathrm{1}\:\mathrm{and}\:\mathrm{then}\:{y}\:=\:−\mathrm{4} \\ $$