x-coordinates where f '(x) = 0

Question

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

Answer 1

f(x) = 2x + sin(2x)

Set f'(x) equal to zero and solve for x.

f'(x) = 2 + 2cos(2x) = 0

2 = -2cos(2x)

cos(2x) = -1

2x = π

x = π/2