Find the x-coordinates where f '(x) = 0 for f(x) = 2x + sin(4x) in the interval [0, π].

Answer 1

dy/dx = 2 + 4 cos 4 x

so
cos 4x = -1/2

4x = 180 - 60 degrees = 120
degrees = (2/3) pi
so x = pi/6
or
4x = 180+60 or 4 pi/3
so x = pi/3
4 x = 360+180 - 60 = 480 =8 pi/3
so x = 2 pi/3
4 x = 360+180 + 60 = 600 = 10 pi/3
so x = 5 pi/6 too big
so
pi/6 , pi/3 , 2 pi/3