Let f ( x ) = l | x |, x^2 , , , , , | x | 2 8 - 2 | x |, , , , ,… - Vidyadip

MCQ

Let $f\left( x \right) = \left\{ \begin{array}{l}
\max \left\{ {\left| x \right|,{x^2}} \right\},\,\,\,\,\left| x \right| \le 2\\
8 - 2\left| x \right|,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2 < \left| x \right| \le 4\,\,\,\,
\end{array} \right.$. Let $S$ be the set of points in the interval $(-4, 4)$ at which $f$ is not differentiable. Then $S$

A
is an empty set
✓
equals $\left\{ { - 2, - 1,0,1,2} \right\}$
C
equals $\{-2, -1, 1, 2\}$
D
equals $\{-2, 2\}$

✓

Answer

Correct option: B.

equals $\left\{ { - 2, - 1,0,1,2} \right\}$

b
From the graph we can easily conclude that $f (x)$ is non -derivable at $x = -2,-1,0,1,2$

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