NIMCET Previous Year Questions (PYQs) – Trigonometry – Page 1 of 5

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:   $\boxed{{\displaystyle 2\text{ points}}}$