I got this question wrong on a test, I am not sure what went wrong.
Verify that the function satisfies the Mean Value Theorem and then find all numbers $c$ that satisfy the conclusion of the Mean Value Theorem.
$f(x) = x + \sin 2x, [0, 2\pi]$
This one I wasn't so sure what to do because I have no idea how to find two values that are equal to each other so I just plugged in $0$ and $2\pi$ and I got $-1$ as the answer which was wrong.