If $f\left(x\right)=\max \left\{\frac{x}{n}, \left|\sin \pi x\right|\right\}, n\in N$ has maximum points of non-differentiability for $x\in (0,\mathrm{ }4)$, then $n$ cannot be

• A

  $4$
• Correct answer
  B

  $2$
• C

  $5$
• D

  $6$

Solution

$f\left(x\right)=\max \left\{\frac{x}{n}, \left|\sin \pi x\right|\right\}$

Thus, for the maximum points of non-differentiability, graphs of $y=\frac{x}{n}$ and $y=\left|\sin \pi x\right|$ must intersect at maximum number of points which occurs when $n>3.5$

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