Recently, the College Board came out with practice session videos where they go over how to solve certain types of problems on the AP Calculus BC test.
In one of those videos (Practice Session 2: FRQ (Calculator Active), they go over a Free Response question involving the polar curve $r(\theta) = \sqrt{\theta}-\cos(\theta)$. Part B goes as follows:
Find the value of $\theta$, for $0 \le \theta \le 2\pi$, when the graph of $r(\theta)$ is furthest from the origin. Justify your answer.
Both I and the video start by finding the critical points.
My calculations were as follows:
$$ r'(\theta) = \frac{1}{2\sqrt{\theta}}-\sin(\theta) $$ $$ 0=r'(\theta) $$
According to my Casio fx-9750GII (using this formula: SolveN(1÷(2√X)=sin X)), these critical points are at $\theta = 0.6618$ and $\theta = 2.8403$. It also spat out some other values which were greater than $2\pi$, but those are irrelevant. I then added the endpoints ($0$ and $2\pi$), coming up with the following list of candidate points:
$$[0, 0.6618, 2.8403, 2\pi]$$
The teachers in the video don't say what formula they used; merely that they calculated the critical points using their calculator (presumably a Ti-84), and came up with the following candidate points:
$$[0, 3.4155518, 6.078975, 2\pi]$$
Our calculations were the same past that point, but we came to different results due to garbage in, garbage out.
I find it very strange that we came to such different results. I'm almost 100% sure that I differentiated the polar function correctly, and I don't see any obvious issues with the formula I entered into my calculator. Thus, here's my question: Did I mess up, or did they mess up? If I was the one who messed up, what did I do wrong?
EDIT: Almost 100% certainty isn't the same as complete certainty. As Amaan M helpfully pointed out, I differentiated it wrong after all.