If $f (x) = | | | x | - 2 | + p |$ has more than $3$ points of non differentiability, then the value of $p$ can be:

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Solution

The correct option is C $- 1$

Clearly, for $p = 0$ $f (x) = | | | x | - 2 | + p |$ will be same as the above graph, and it is non differentiable for exactly $3$ points.
Now, for more than $3$ points of non differentiability, we need need to shift the graph down and then take the modulus.
$∴$ We need to shift the graph of $| | x | - 2 |$ down. So, $p$ has to be negative. i.e $p < 0$

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If f(x)=|||x|−2|+p| has more than 3 points of non differentiability, then the value of p can be:

If $f (x) = | | | x | - 2 | + p |$ has more than $3$ points of non differentiability, then the value of $p$ can be: