Critical Points of a trig function

[realism877]

Trig function:-sinx+(1/2)sin2x(2)

The criticial points are (pi), (pi/3), and (5pi/3).

Am I correct?

 

[QuarkCharmer]

Is that the first derivative there, or is it not differentiated?
$$-sin(x)+2sin(2x)$$

 

[realism877]

Yes, the first derivative.

 

[QuarkCharmer]

Well,
Given that $sin(2x) = 2sin(x)cos(x)$, you could say the following:
$4sin(x)cos(x)-sin(x)=0$
$sin(x)(4cos(x)-1)=0$
Using the zero product property, what are the solutions to that?

 

[realism877]

I just want to know if my critical points are correct or not.

 

[QuarkCharmer]

No, they are not

 

[realism877]

Is pi/2 a point instead of pi?

 

[realism877]

I'm sorry.

The derivative is sin2x-sinx

 

[QuarkCharmer]

I'm sorry.

The derivative is sin2x-sinx

In that case you were right.