A function f is defined on [-3, 3] as f(x) = begincases min |x|, 2 - x2 -2 le x le 2 [|x|], &2

Question

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 . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

f(x) = begincases min |x|, 2 - x2 -2 le x le 2 [|x|], &2 < |x| le 3 endcases ⇒ x ∈ [-3, -2) ∪(2, 3] <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/9d7c33f2c7e13acf15ce90918de200f5-.png" /> Number of points of non-differentiability in (-3,3)=5

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

$f (x) = {min {∣ x ∣, 2 - x^{2}}, [∣ x ∣], - 2 \leq x \leq 2 2 < ∣ x ∣ \leq 3$

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

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

Q. A function f is defined on [−3,3] as f(x)={min{∣x∣,2−x2},[∣x∣],​−2≤x≤22<∣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−x2},[∣x∣],​−2≤x≤22<∣x∣≤3​ ⇒x∈[−3,−2)∪(2,3] Number of points of non-differentiability in (−3,3)=5

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

$f (x) = {min {∣ x ∣, 2 - x^{2}}, [∣ x ∣], - 2 \leq x \leq 2 2 < ∣ x ∣ \leq 3$

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

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