Question

Giving medal immediately after answer.
Find the x-coordinates where f '(x) = 0 for f(x) = 2x + sin(2x) in the interval [0, 2π].

Answer 1

f'(x)=2+2cos 2x=0
1+cos 2x=0
cos 2x=-1=cos(2n+1) pi
2x=(2n+1)pi
\[x=\left( 2n+1 \right)\frac{ \pi }{ 2 }\]
where n is an integer.
n=0,1
x=?