Question

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

Over what interval in this period is the curve concave up? Please show work if at all possible

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, ( \pi )/(3)]` U
`[( 5\pi )/(3),2\pi]`