1. Tardigrade
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  3. Mathematics
  4. A function f is defined on [-3, 3] as f(x) = begincases min |x|, 2 - x2 -2 le x le 2 [|x|], &2 < |x| le 3 endcases where [x] denotes the greatest integer le x. The number of points, where f is not differentiable in (-3, 3) is .

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Q. A function $f$ is defined on $[-3, 3]$ as
$f(x) = \begin{cases} \min \{|x|, 2 - x^2\}, & -2\le x \le 2 \\ [|x|], &2 < |x| \le 3 \end{cases}$
where $[x]$ denotes the greatest integer $\le x$. The number of points, where f is not differentiable in $(-3, 3)$ is ______.

JEE MainJEE Main 2021Continuity and Differentiability

Solution:

$f(x) = \begin{cases} min \{|x|, 2 - x^2\}, & -2\le x \le 2 \\ [|x|], &2 < |x| \le 3 \end{cases}$

$\Rightarrow x \in [-3, -2) \cup(2, 3]$
image
Number of points of non-differentiability in $(-3,3)=5$