Let f: (- 1, 1) → R be a function defined by f(x) = max \ - |x|, - 1 - x^ 2 \ . If K be the set of all points at which f is not differentiable, then K has exactly

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Continuity and Differentiability

NTA Abhyas 2020 · Mathematics · Continuity and Differentiability

Let f: (- 1, 1) → R be a function defined by f(x) = max \ - |x|, -...

Let

f: \left(- 1, 1\right) \to R

be a function defined by

f\left(x\right) = max \left\{- \left|x\right|, - \sqrt{1 - x^{2}}\right\}.

K

be the set of all points at which

f

is not differentiable, then

K

has exactly $Let f: (- 1, 1) → R be a function defined by f(x) = max \ - |x|, - 1 - x^ 2 \ . If K be the set of all points at which$

Options

Atwo elements
Bone element
Cthree elements
Dfive elements

Correct answer

C. three elements

Step-by-step solution

$Let f: (- 1, 1) → R be a function defined by f(x) = max \ - |x|, - 1 - x^ 2 \ . If K be the set of all points at which$

From the graph it can be concluded that&

f ( x )

is non-differentiable at

x = 0, \pm \dfrac{1}{\sqrt{2}}

in ( - 1, 1 )

i.e., at

3

points in

\left(- 1, 1\right)

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