Now solve for f'(x) = 0
Can you do it?
Find the critical numbers of the function on the interval 0 ≤ θ < 2π.
f(θ) = 2cos(θ) + (sin(θ))^2
I know the smaller value of θ=0, but how would you find the larger value or the other critical number?
What you have to do is to factorise to get all the answers. Let me rearrange.
Now, you set both to zero, and you get:
You get 5 solutions in all. You already have 2, that is 0 and pi
3 more to go! Post what you get.
Moderator edit: I'd like to see the OP's working before the things I have deleted are posted.