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Continuity and Differentiability
NCERT Class 12
CBSE
Grade 12
Question:
The function $f(x) = |x - 1|$ is: (a) Continuous everywhere, but not differentiable at $x = 1$ (b) Differentiable everywhere (c) Discontinuous at $x = 1$ (d) Neither continuous nor differentiable at $x = 1$
Step-by-Step Solution
Continuous on $\mathbb{R}$, LHD $ eq$ RHD at $x=1 \Rightarrow$ Not differentiable at $x=1$. [1.0 Mark]
--- 🎯 Official CBSE Marking Scheme: Selecting Continuous everywhere, but not differentiable at $x=1$: 1.0 Mark
Correct Answer:Continuous everywhere, but not differentiable at $x = 1$
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