Help on calculus please!

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)

f’(x) = 2 + 2cos(2x)

Set equal time 0 to find the x-coordinate:

0 = 2 + 2cos(2x)

-2 = 2cos(2x)

-1 = cos(2x)

cos^-1(-1) = π

So 2x = π

So x = π/2

x = 3π/2 also works. Cos(2(3π/2)) = cos(3π) = cosπ = -1