Number of point of which f(x) is not differentiable f(x)=|cosx|+3 in [-π, π]

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Question Id : 11535 | Context :NIMCET 2023

Number of point of which f(x) is not differentiable

$f(x)=|cosx|+3$ in

$[-\pi, \pi]$

🎥 Video solution / Text Solution of this question is given below:

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

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