Why on Earth would you try to find the arc-cosine of -3/2?! The Domain of arccos(x) is [-1,1]. Never do that again.
I can't figure this out at all, I've got the derivative
and the domain of the function is
I've factorised to get
But when I put the second bracket as zero to find for that bracket I get
which doesn't get me anywhere on my calculator.
Have I made a mistake somewhere?
Sorry but I am still learning.
I'm pretty sure my factorising is correct, and making the first bracket equal to zero is giving me
which gives me one stationary point, but for the second bracket, like you say, I'm outside of the domain for arccos.
What kind of help do you need? You have correctly determined that the derivative is 0 only when 2 cos(x)- 1= 0 or when 2cos(x)+ 3= 0. Since the range of cosine is -1 to 1, there is NO value of x that makes 2cos(x)+ 3= 0 so the only possible critcal point is where 2 cos(x)- 1= 0.