Question

Find the x-coordinates where f '(x) = 0 for f(x) = 2x – sin(2x) in the interval [0, 2π].

Answer 1

0; π and 2π.

Explanation:

1) if f(x)=2x-sin2x, then f'(x)=2-2cos2x;

2) if f'(x)=0, then 2-2cos2x=0,

cos2x=1; ⇒ x=πn, n∈Z;

3) if the given interval is [0;2π] and x=πn (n∈Z), then x=0; π; 2π.