finding the max of a trig function

Question

f(x) = 5sin (-4x)-3 in the domain 0<x<2 pi

i know how to find the derivative

f'(x) = -20 cos (-4x)

 

but i am unsure as to how you solve this for critical values:

0=-20cos(-4x)

 

(maximum is 2)

Answer 1

0=-20cos(-4x)

0 = cos(-4x) = cos(4x)

4x = 0 or 3pi/2 or 2pi or 7pi/2 or ...

x=0 or x =3p/8 or x=pi/2 or 7pi/8 or 5pi/2 or ....

only x=3pi/8 or pi/2 or 7pi/8 is within the limits. 0 is just outside the limit 5pi/2 > 2pi