If f(x) = max \ (x)/(n), | |\ , n ∈ ℕ has maximum points of...

f\left(x\right) = max \left\{\dfrac{x}{n}, \left|\sin \pix\right|\right\}, n \in \mathbb{N}

has maximum points of non-differentiability for

x \in (0,4)

, then

n

cannot be $If f(x) = max \ (x)/(n), | |\ , n ∈ ℕ has maximum points of non-differentiability for x ∈ (0,4) , then n cannot be$

Options

A $4$
B $2$
C $5$
D $6$

Correct answer

B. $2$

Step-by-step solution

f\left(x\right) = max \left\{\dfrac{x}{n}, \left|\sin \pix\right|\right\}

$If f(x) = max \ (x)/(n), | |\ , n ∈ ℕ has maximum points of non-differentiability for x ∈ (0,4) , then n cannot be$
Thus, for the maximum points of non-differentiability, graphs of

y = \dfrac{x}{n}

and

y = \left|\sin \pix\right|

must intersect at maximum number of points which occurs when

n > 3.5

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