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

• A

  $5$
• Correct answer
  B

  $3$
• C

  $2$
• D

  $4$

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)

Hence, the correct answer is option: 'B'.