Expert: Abe Mantell - 12/29/2007

Question
Hello. I'm having trouble with this problem.
Find all extrema in the interval [0,2π] if y= x + sin x

Answer
Hello Joyice,

First, y'=1+cos(x)...solving y'=0 gives: cos(x)=-1
Thus, x=pi, for x in [0,2pi], with y''=-sin(x), y''(pi)=0
But, y'(pi-)>0 and y'(pi+)>0
So, at x=pi we have a point of inflection.
Thus, no extrema between 0 and 2pi...the extrema must be
at the end-points: at x=0 and x=pi

OK?

TTYL, Abe

BTW: I've never seen your name (Joyice) before!!!
    Only "Joyce"...what kind of name is "Joyice"?