Question

Find the greatest and the least values of the following functions (292-296).
$f\left(x\right)=co{s}^{2}x+cosx+3$

Answer 1

$f\left(x\right)={\cos }^{2}x+cosx+3$

$f^1\left(x\right)=2cosx(-sinx)-sinx$$=0$

$-sinx(2cosx+1)=0$

$x=0$ or $cosx=-\frac{1}{2}$

$x={\cos }^{-1}(-\frac{1}{2})$

$x=\frac{2\pi }{3}$

greatest value at $x=0$

and least at $x=\frac{2\pi }{3}$