f(x)=4sin(x)+cos(2x) now take derivative
f'(x)=4cos(x)-2sin(2x) observe that sin(2x)=2sin(x) cos(x) leads to
f'(x)=4cos(x)-4sin(x)cos(x) now equate to zero
4cos(x)-4sin(x) cos(x)=0 then
cos(x)=0 which gives x=Pi/2
or sin(x)=1 which also gives that x=pi/2
Now check this critical point x=Pi/2 and the endpoints x=0 and x=Pi
by substitution in f(x) we find that f(0)=f(Pi)=1 and f(Pi/2)=3
Salam
