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Find the number of points of discontinuity

Source: MTRP 2016 Class 11-Multiple Choice Question: Problem 12 :-

May 31, 2020
functioncontinuity

Problem Statement

Let f(x)=(x−1)(x−2)(x−3)f(x)=(x-1)(x-2)(x-3). Consider g(x)=min{f(x),f′(x)}g(x)=min\{f(x),f'(x)\}. Then the number of points of discontinuity are
[*] 0 [*] 1 [*] 2 [*] More than 2
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