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 pos
Mathematics
taylor210
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
Over what interval in this period is the curve concave up? Please show work if at all possible
1 Answer

1. User Answers apologiabiology
period is from 0 to 2pi
take the deritivive then take it again
we get f''(x)=4cosĀ²(x)2cos(x)+2
it is negative between 0 and pi/3 and also between 5pi/3 and 2pi
concave down in the interval
[tex][0, \frac{ \pi }{3}][/tex] U [tex][\frac{ 5\pi }{3},2\pi][/tex]