1. ## Critical values.

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?

2. Differentiate:

$\displaystyle f'(x) = -2\sin\theta + 2\cos\theta\sin\theta$

Now solve for f'(x) = 0

$\displaystyle 0 = -2\sin\theta + 2\cos\theta\sin\theta$

Can you do it?

3. I got pi for the larger theta value, is this correct?

4. What you have to do is to factorise to get all the answers. Let me rearrange.

$\displaystyle 0 = 2\cos\theta\sin\theta -2\sin\theta$

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.

5. Originally Posted by ioke09
I got pi for the larger theta value, is this correct?
Giving your answers without showing the working that led to them is usually not very productive for getting feedback (unless you are happy with replies like "Wrong" or "You have not found all solutions" etc.)