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Graph of |x|

The number of...

Question

The number of integral values of $^{'} a^{'}$ so that $f (x) = | | | x | - 2 | + a |$ has exactly $7$ point of non differentiablility $\forall x ϵ R$ is

0

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1

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3

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infinite

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Solution

The correct option is B $1$
Clearly from the graph,
to have $7$ points of non -differentiability
$2 + a > 0 ⟹ a > - 2$
and $a < 0$
Thus only possible solution is $a = - 1$

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