Question Number 22332 by A1B1C1D1 last updated on 15/Oct/17
Answered by ajfour last updated on 15/Oct/17
![((d[f(x)])/dx)=1+2cos x=0 ⇒ cos x=−(1/2) x=2nπ±((2π)/3) where n∈Z . which is equivalent to x=(2n+1)π±(π/3) .](Q22334.png)
$$\frac{{d}\left[{f}\left({x}\right)\right]}{{dx}}=\mathrm{1}+\mathrm{2cos}\:{x}=\mathrm{0} \\ $$$$\Rightarrow\:\mathrm{cos}\:{x}=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:\:\:{x}=\mathrm{2}{n}\pi\pm\frac{\mathrm{2}\pi}{\mathrm{3}}\:\:{where}\:{n}\in\mathbb{Z}\:. \\ $$$$\:\:\:\:{which}\:{is}\:{equivalent}\:{to} \\ $$$$\:\:\:\:{x}=\left(\mathrm{2}{n}+\mathrm{1}\right)\pi\pm\frac{\pi}{\mathrm{3}}\:. \\ $$
Commented by A1B1C1D1 last updated on 16/Oct/17
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{very}\:\mathrm{much}. \\ $$
Commented by A1B1C1D1 last updated on 15/Oct/17
$$\mathrm{Hello},\:\mathrm{the}\:\mathrm{correct}\:\mathrm{answere}\:\mathrm{is}\::\:\left(\mathrm{2n}\:+\:\mathrm{1}\right)\pi\:\pm\:\frac{\pi}{\mathrm{3}} \\ $$
Commented by ajfour last updated on 15/Oct/17
$${same}\:{locations}\:{either}\:{way}. \\ $$