Differentiate:
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.
Factorise:
Moderator deletion.
Now, you set both to zero, and you get:
Moderator deletion.
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.