Question

Consider f(x)=cos^2x+2cosx over one complete period beginning with x=0

Answer 1

Period is from 0 to 2pi

take the deritivive then take it again
we get f''(x)=-4cos²(x)-2cos(x)+2


it is negative between 0 and pi/3 and also between 5pi/3 and 2pi

concave down in the interval
$[0, \frac{ \pi }{3}]$ U $[\frac{ 5\pi }{3},2\pi]$