GATE 2023 MN – Question 40
For $f(x)=|x|+|x-1|$ and real x, which statement is correct?
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Show answer and explanation
Correct answer: (B) Continuous and nondifferentiable at two points
Explanation
Both absolute-value terms are continuous. The piecewise function is 1−2x for x<0, 1 for 0≤x≤1, and 2x−1 for x>1. Slopes change from −2 to 0 at x=0 and from 0 to 2 at x=1. It is therefore continuous but nondifferentiable at two points, B.