Find the critical numbers of the function on the interval 0 ≤ θ

Question

Find the critical numbers of the function on the interval 0 ≤ θ < 2π.
f(θ) = 2cos(θ) + (sin(θ))^2

anonymous · Answer

$$f'(x)= -2\sin(x) + 2\sin(x) * \cos(x)$$
**factor**
$$f'(x)= 2\sin(x)[-1+\cos(x)]$$

2sin(x)=0 :::: when sin(x)=0
sin(x)=0 when x=k(pi), and k=0,1,2...

-1+cos(x)=0 :::: when cos(x)=1
cos(x)=1 when x=k(pi), and k=0,1,2...

So what are the CN on interval 0<x<2(pi)???

Help!

anonymous · Answer

I got one of them.. 0

Can't find the other.... hmm

hero · Answer

What is CN?

myininaya · Answer

critical numbers

hero · Answer

Oh

hero · Answer

I'm sleepy and don't feel like doing trig right now

myininaya · Answer

sin(x)=0 when x=0,pi
cos(x)=1 when x=0
the only critical numbers btw 0 and 2pi including 0 is 0 and pi

myininaya · Answer

by the way you solved cos(x)=1 wrong
cos(odd integer * pi) is not 1

anonymous · Answer

Got it, thanks!

anonymous · Answer

I have a quick concept questions. DO you mind if i ask you?

anonymous · Answer

Requires no work really, just a concept i'm confused about..

anonymous · Answer

nvm figured it out