taylor210 taylor210

01-02-2017
Mathematics

Answered

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

Verified Answer :

apologiabiology apologiabiology

01-02-2017

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 \([\frac{ 5\pi }{3},2\pi]\)

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