A function f is defined on [ - 3 , 3 ] as f x = 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 ___ .

f x = 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

Mathematics - Continuity - Differentiability Question with Solution | TestHub

MathematicsContinuity - DifferentiabilityDifferentiabilityHard2 minPYQ_2021

MathematicsHardnumerical

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 ___ .

Answer:

5.00

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 $(- 3, 3) = 5$

Stream:JEESubject:MathematicsTopic:Continuity - DifferentiabilitySubtopic:Differentiability

⏱ 2mℹ️ Source: PYQ_2021

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