f:-1,1→R be a function defined by fx= x^2cos(π)/x for x≠0 0 for x=0 The set of points where f is not differentiable is

Correct answer: (C) x∈-1,1:x=2/(2n+1),n∈Z. We have, fx= x^2cos(π)/x for x≠0 0 for x=0 fx is not differentiable at cos(π)/x=0 cos(π)/x=0⇒(π)/x=2n+1(π)/2 ⇒x=2/(2n+1) ∵fx is not differentiable at x∈-1,1:x=2/(2n+1),n∈Z

Q43 / 91 · KVPY 2018 (SB/SX) · Mathematics

$f : [- 1, 1] \to R$ be a function defined by $f (x) = \{\begin{matrix} x^{2} |\cos (\frac{π}{x})| & for x \neq 0 \\ 0 & for x = 0 \end{matrix}$ The set of points where $f$ is not differentiable is

A
${x \in [- 1, 1] : x \neq 0}$
B
{ $x \in [- 1, 1] : x = 0$ or $x = \frac{2}{2 n + 1}, n \in Z$ }
Correct answer
C
$\{x \in [- 1, 1] : x = \frac{2}{2 n + 1}, n \in Z\}$
D
$[- 1, 1]$

Solution

We have,

$f (x) = \{\begin{array}{cl} x^{2} |\cos (\frac{π}{x})| & for x \neq 0 \\ 0 & for x = 0 \end{array}$

$f (x)$ is not differentiable at $|\cos \frac{π}{x}| = 0$

$\cos \frac{π}{x} = 0 \Rightarrow \frac{π}{x} = (2 n + 1) \frac{π}{2}$

$\Rightarrow x = \frac{2}{2 n + 1}$

$∵ f (x)$ is not differentiable at

$x \in [- 1, 1] : x = \frac{2}{2 n + 1}, n \in Z$

Hence, the correct answer is option: 'C'.

f:-1,1→R be a function defined by fx=x2cosπx for x≠00 for x=0 The set of points where f is not differentiable is

Solution

More Continuity and Differentiability Questions

$f : [- 1, 1] \to R$ be a function defined by $f (x) = \{\begin{matrix} x^{2} |\cos (\frac{π}{x})| & for x \neq 0 \\ 0 & for x = 0 \end{matrix}$ The set of points where $f$ is not differentiable is