Points of Non-Differentiability of \( f(x) = |\cos x| + 3 \)

Step 1: \( \cos x \) is differentiable everywhere, but \( |\cos x| \) is not differentiable where \( \cos x = 0 \).

Step 2: In the interval \( [-\pi, \pi] \), we have:

\[ \cos x = 0 \Rightarrow x = -\frac{\pi}{2},\ \frac{\pi}{2} \]

So \( f(x) = |\cos x| + 3 \) is not differentiable at these two points due to sharp turns.

✅ Final Answer:   \( \boxed{2 \text{ points}} \)