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

Correct answer: 5. fx= min|x|,2-x^2,-2≤x≤2 [|x|] , 2<|x|≤3 ⇒x∈[-3,-2)∪(2,3] Number of points of non-differentiability in -3,3=5

Q55 / 90 · JEE Main 2021 (25 Feb Shift 2) · Mathematics

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

Correct answer: 5

Solution

$f (x) = \{\begin{matrix} \min \{| x |, 2 - x^{2}\}, - 2 \leq x \leq 2 \\ [| x |], 2 < | x | \leq 3 \end{matrix}$
$\Rightarrow x \in [- 3, - 2) \cup (2, 3]$
Number of points of non-differentiability in $(- 3, 3) = 5$

Hence, the correct answer is 5.

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A function f is defined on [-3,3] asfx=min|x|,2-x2,-2≤x≤2[|x|] , 2<|x|≤3where [x] denotes the greatest integer ≤x. The number of points, where f is not differentiable in -3,3 is ___ .

Solution

Relevant Questions

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