Mathematics

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

1 Answer

  • 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]
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