A function f is defined on [-3,3] as f(x)= cc |x|, 2-x^ 2 & , -2 … - Vidyadip

MCQ

A function $f$ is defined on $[-3,3]$ as

$f(x)=\left\{\begin{array}{cc}\min \left\{|x|, 2-x^{2}\right\} & , \quad-2 \leq x \leq 2 \\ {[|x|]} & , \quad 2<|x| \leq 3\end{array}\right.$

where $[x]$ denotes the greatest integer $\leq x .$ The number of points, where $f$ is not differentiable in $(-3,3)$ is

A
$10$
B
$2$
✓
$5$
D
$8$

✓

Answer

Correct option: C.

$5$

c
$f(x)=\left\{\begin{array}{cc}\min \left\{|x|, 2-x^{2}\right\} & , \quad-2 \leq x \leq 2 \\ {[|x|]} & , \quad 2<|x| \leq 3\end{array}\right.$

$\Rightarrow x \in[-3,-2) \cup(2,3]$

Number of points of non-differentiability in $(-3,3)=5$

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