Here is the question I'm having trouble with. Apparently the answer is A.
You need to find the derivative at $\displaystyle x=k$
But, the trick is that this an absolute value function.
The regular sine is negative in that interval
So you need to find the derivative of,
$\displaystyle y=-\sin x$
$\displaystyle y'=-\cos x$
At, k:
$\displaystyle -\cos k$