A function f is defined on [ - 3, 3 ] as f(x) = \ array ll min\ | x | , 2 - x ^ 2 \ , - 2 ≤ x ≤ 2 [ | x | ] , 2 where [ x ] denotes the greatest integer ≤ x . The number of points, where f is not differentiable in (- 3

Correct answer: 0 f(x) = \ array ll min\ | x | , 2 - x ^ 2 \ , - 2 ≤ x ≤ 2 [ | x | ] , 2 ⇒ x ∈ [ - 3, - 2 ) ( 2, 3 ] Number of points of non-differentiability in (- 3, 3) = 5

JEE Main 202125 FebruaryEvening Shift

Exam: JEE Main
Year: 2021
Date: 25 February
Shift: Evening Shift
Subject: Mathematics
Chapter: Continuity and Differentiability

JEE Main 2021 · 25 February · Evening Shift · Mathematics · Continuity and Differentiability

A function f is defined on [ - 3, 3 ] as f(x) = \ array ll min\ | x...

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

$f\left(x\right) = \left\{$ $\begin{array}{ll}min\left\{| x | , 2 - {x}^{2}\right\}, - 2 \le x \le 2 \\ [ | x | ] , 2 < | x | \le 3\end{array}$ $\right</p><p>where$ [ x ] $denotes the greatest integer$ \le x $. The number of points, where$ f $is not differentiable in$ \left(- 3, 3\right)$ is ___ .

$A function f is defined on [ - 3, 3 ] as f(x) = \ array ll min\ | x | , 2 - x ^ 2 \ , - 2 ≤ x ≤ 2 [ | x | ] , 2 where [$

Correct answer

Step-by-step solution

$f\left(x\right) = \left\{$ $\begin{array}{ll}min\left\{| x | , 2 - {x}^{2}\right\}, - 2 \le x \le 2 \\ [ | x | ] , 2 < | x | \le 3\end{array}$ $\right</p><p>$ ⇒ x \in [ - 3, - 2 ) \cup ( 2, 3 ]$
$A function f is defined on [ - 3, 3 ] as f(x) = \ array ll min\ | x | , 2 - x ^ 2 \ , - 2 ≤ x ≤ 2 [ | x | ] , 2 where [$
Number of points of non-differentiability in \left(- 3, 3\right) = 5

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