Let $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ be a function defined by $f(x)=\|x+2|-2| x\|$. If $m$ is…

Let $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ be a function defined by $f(x)=\|x+2|-2| x\|$. If $m$ is the number of points of local minima and $n$ is the number of points of local maxima of $f$, then $m+n$ is
  1. $5$
  2. $3$
  3. $2$
  4. $4$

Solution

$f(x)=\|x+2|-2| x\|$
Critical points, $0,-2,2,-\frac{2}{3}$

No. of maxima $=1$
No. of minima $=2$
option (2)

Asked in: JEE Main 2025 (03 Apr Shift 2)

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