Answer
Yes, see explanations.
Work Step by Step
Step 1. Theorem 2 states that if $f$ has a local maximum or minimum value at an interior point $c$ of its domain and if $f'$ is defined at $c$, then $f'(c)=0$.
Step 2. In the case of $f(x)=|x|$, it has a minimum at $x=0$, but $f'(0)\ne0$. However, this does not contradict with Theorem 2 because in this case $f'(0)$ is undefined, and this means that Theorem 2 does not apply to this case.
Step 3. We conclude that the result in this case is consistent with Theorem 2.
