Identify the increasing and decreasing intervals and identify the relative extrema.

Question

precal · Answer

$$f(\theta)=\theta+2\sin$$
on $$\left( 0,2 \pi \right)$$

precal · Answer

I took the first derivative and set it equal to zero to solve it

precal · Answer

$$f ' =1+2\cos  \theta $$

precal · Answer

$$\theta=\frac{ 11 \pi }{ 6},\frac{ 7 \pi  }{ 6}$$

precal · Answer

am I overlooking another solution because when I did a sign analysis, I notice that between these two values and using the unit circle cosine is negative and positive in that region

precal · Answer

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zepdrix · Answer

$\Large\rm f(\theta)=\theta+2\sin\theta$
Your derivative looks good,
$\Large\rm f'(\theta)=1+2\cos\theta$
Your critical points do not.
That's probably what is giving you trouble.

Cosine is 1/2 at ummm pi/3.
So our negative 1/2 will be at 2pi/3 and 4pi/3.

precal · Answer

yes thanks so much that is my issue