f (x)= x - 2sinx, 0<x<2pi (less than or equal to)
Regarding this problem, I think that I have it solved. I just need someone to check my work to make sure I got the correct answer. Here is my answer:
f ' (x)= 1 - 2cosx ; 1-2cosx=0; cosx= 1/2
cosx > 1/2
f is increasing from (0, pi/3) and (5pi/3, 2pi)
f is decreasing from (pi/3, 5pi/3)
f ''(x) = 2sinx; sinx = 0; sinx>0
(0 , 2pi)
concave up: (pi, 2pi)
concave down: (0, pi)
Feedback would be appreciated, thanks.
given
and
<-----a--neg--b--pos--c--neg--d---->
f is decreasing from 0 to and from to
if is increasing from to
[tex]0=2sin(x) => sin(x)=0 =>
and
<---a--pos--b--neg--c--->
f is concaved up from 0 to
f is concaved down from to
Edit: You can see the graph here:
http://www.wolframalpha.com/input/?i=plot+x-2sin%28x%29
Look at it and you will see that my claims are verified.