Question Number 84627 by M±th+et£s last updated on 14/Mar/20
![1)∣sec(x)∣<2tan(x) on[0,2π] 2)find the cirtical points and the range of f(x)=∣x−3∣+∣2x+1∣](https://www.tinkutara.com/question/Q84627.png)
$$\left.\mathrm{1}\right)\mid{sec}\left({x}\right)\mid<\mathrm{2}{tan}\left({x}\right)\:{on}\left[\mathrm{0},\mathrm{2}\pi\right] \\ $$$$ \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{cirtical}\:{points}\:{and}\:{the}\:{range}\:{of} \\ $$$${f}\left({x}\right)=\mid{x}−\mathrm{3}\mid+\mid\mathrm{2}{x}+\mathrm{1}\mid \\ $$$$ \\ $$
Commented by TANMAY PANACEA last updated on 14/Mar/20
$${what}\:{is}\:{wuestion}\:{no}\:\mathrm{1} \\ $$
Commented by M±th+et£s last updated on 14/Mar/20
$${solve}\:{the}\:{inequality} \\ $$
Answered by TANMAY PANACEA last updated on 14/Mar/20
$$\left.\mathrm{2}\right)\:{f}\left({x}\right)=\mid{x}−\mathrm{3}\mid+\mid\mathrm{2}{x}+\mathrm{1}\mid \\ $$$${critical}\:{value}\:{of}\:{x}\:{are}\:\mathrm{3},−\mathrm{0}.\mathrm{5} \\ $$$${f}\left({x}\right)\:={x}−\mathrm{3}+\mathrm{2}{x}+\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:=\mathrm{3}{x}−\mathrm{2}\:\:\:\:\:{when}\:{x}>\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:=\mathrm{7}\:\:\:\:\:\:\:{when}\:{x}=\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:=−\left({x}−\mathrm{3}\right)−\left(\mathrm{2}{x}+\mathrm{1}\right)\:\:\:{x}<−\mathrm{0}.\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=−\mathrm{3}{x}+\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{3}.\mathrm{5}\:\:\:{when}\:{x}=−\mathrm{0}.\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=−\left({x}−\mathrm{3}\right)+\mathrm{2}{x}+\mathrm{1}\:\:\:{when}\:\:\mathrm{3}>{x}>−\mathrm{0}.\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:={x}+\mathrm{4} \\ $$$${so}\:{f}\left({x}\right)\in\left[\mathrm{3}.\mathrm{5},\infty\right) \\ $$$$ \\ $$$$ \\ $$
Commented by jagoll last updated on 14/Mar/20
