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JEE Main 2021 · Mathematics · Differentiation and Application of Derivatives · easy

The number of points in mathbb R at which f(x)=|x^2-3x+2|+|x-3| is not differentiable is

Single correct option

The number of points in R\mathbb R at which f(x)=∣x2−3x+2∣+∣x−3∣f(x)=|x^2-3x+2|+|x-3| is not differentiable is
  1. A. 11
  2. B. 22
  3. C. 44
  4. D. 33
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Answer: (D) 33

Non-differentiability can occur only where an absolute-value expression vanishes. x2−3x+2=(x−1)(x−2)x^2-3x+2=(x-1)(x-2) vanishes at x=1,2x=1,2, and it changes sign there, so the first term has kinks at both points. The term ∣x−3∣|x-3| has a kink at x=3x=3, where the first term equals 2≠02\ne0 and is smooth. No kinks cancel, so there are 33 points.
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