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Number of local maxima and minima of a function with modulus

This type of question, asked 2 times: 25 Jun 2022, 3 Apr 2025. All 2 questions below, oldest first.

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  1. Question 1

    25 Jun 2022

    178
    Let f(x)=∣(x−1)(x2−2x−3)∣+x−3,x∈Rf(x) =\left| (x- 1)\left( x^{2}- 2x- 3 \right) \right|+x- 3,x\in R. If mm and MM are respectively the number of points of local minimum and local maximum of ff in the interval (0,4)(0,4), then m+Mm + M is equal to

  2. Question 2

    3 Apr 2025

    126
    Let f:R→Rf:R\rightarrow R be a function defined by f(x)=∣∣x+2∣−2∣x∣∣f(x) = \left| |x+ 2| - 2|x| \right|. If mm is the number of points of local minima and nn is the number of points of local maxima of ff, then m+nm+n is.

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