Question Number 79320 by jagoll last updated on 24/Jan/20
$$\mathrm{what}\:\mathrm{the}\:\mathrm{minimum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{y}\:=\:\mathrm{sec}\:\left(\mathrm{x}\right)+\mathrm{cosec}\:\left(\mathrm{x}\right)? \\ $$
Commented by mr W last updated on 24/Jan/20
$${y}=\frac{\mathrm{1}}{\mathrm{sin}\:{x}}+\frac{\mathrm{1}}{\mathrm{cos}\:{x}} \\ $$$${it}\:{has}\:{no}\:{maximum}\:{and}\:{no}\:{minimum}, \\ $$$${since}\:{e}.{g}.\:{when}\:\mathrm{sin}\:{x}\Rightarrow\mathrm{1}\:{we}\:{have}\: \\ $$$$\mathrm{cos}\:{x}\rightarrow\mathrm{0}\:{and}\:{y}\rightarrow\pm\infty. \\ $$$${but}\:{you}\:{can}\:{find}\:{local}\:{maximum}\:{or} \\ $$$${local}\:{minimum}\:{by}\:{using}\:{y}'=\mathrm{0}. \\ $$
Commented by jagoll last updated on 25/Jan/20
$$\mathrm{how}\:\mathrm{to}\:\mathrm{distinguish}\:\mathrm{the}\: \\ $$$$\mathrm{maximum}\:\mathrm{value}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{maximum}\:\mathrm{local}\:\mathrm{value}\:\mathrm{mister}? \\ $$
Commented by mr W last updated on 25/Jan/20
https://www.mathsisfun.com/algebra/functions-maxima-minima.html