Ok I'm supposed to find the asymptotes, the critical numbers, the inflection points for this function. I tried to solve for the x-int and everything went downhill from there.

y=2(cosx)^2 - sinx

I got my x-int to be (1+-sqrt(17))/-4 lol I don't know if thats right at all.

I put 2(1-(sinx)^2) - sinx = 0 then tried to use the quadratic formula to solve for x. Came out ugly

Got my y-int as 2, just set the x = 0 ...

y' was 4(cosx)(-sinx) -cosx but i couldnt solve that = 0 to find the critical numbers... I think two of them are pi/2 and -pi/2 but... yeah. I'm stuck.

Any help would be GREATLY appreciated. Thank you so much.