f(x)=\ array cc 4 & -∞ < x < - 5 x^2-1 & - 5 ≤ x ≤ 5 4 & 5 ≤ x < ∞ array . If k is the number of points where f(x) is not differentiable then k-2=

Correct answer: C. 0 Here f(x) is continous x ∈ R Now At x=- 5 L.H.D = 0 R.H.D =2 x=-2 5 f(x) is not differentiable at x=- 5 At x= 5 L.H.D. =2 x=2 5 R.H.D. =0 f(x) is not differentiable at x= 5 k=2k-2=2-2=0

BITSAT 2024Paper 1

Exam: BITSAT
Year: 2024
Paper: Paper 1
Subject: Mathematics
Chapter: Continuity and Differentiability

BITSAT 2024 · Paper 1 · Mathematics · Continuity and Differentiability

f(x)=\ array cc 4 & -∞ < x < - 5 x^2-1 & - 5 ≤ x ≤ 5 4 & 5 ≤ x < ∞...

f(x)=\left\{

\begin{array}{cc}4 & -\infty < x < -\sqrt{5} \\ x^2-1 & -\sqrt{5} \leq x \leq \sqrt{5} \\ 4 & \sqrt{5} \leq x < \infty\end{array}

\right.

k

is the number of points where

f(x)

is not differentiable then

k-2=

Options

A $2$
B $1$
C $0$
D $3$

Correct answer

C. $0$

Step-by-step solution

Here

f(x)

is continous

\forall x \in \mathbf{R}

Now At

x=-\sqrt{5}

L.H.D = 0 R.H.D

=2 x=-2 \sqrt{5}\Rightarrow \mathrm{f}(\mathrm{x})

is not differentiable at

\mathrm{x}=-\sqrt{5}

x=\sqrt{5}

L.H.D.

=2 x=2 \sqrt{5}

R.H.D.

=0\Rightarrow \mathrm{f}(\mathrm{x})

is not differentiable at

\mathrm{x}=\sqrt{5}\Rightarrow \mathrm{k}=2k-2=2-2=0

Practice Continuity and Differentiability on Quantrex Academy →

More from Continuity and Differentiability

Let f be the function defined by f(x)=\ array cc (x^2-1)/(x^2-2|x-1|-1), & x ≠ 1 (1)/(2)… BITSAT 2024 If f(x)=\ array cc (x^2 ( x))/( (1+x)), & x ≠ 0 0, & x=0 array . , then at x=0, f(x) is BITSAT 2024 Let f be the function defined by f(x)=\ array ll x^ 2 -1 x^ 2 -2|x-1|-1 , & x ≠ 1 1 / 2… BITSAT 2020 Let f(x) = \ array ll x^ p (1)/(x), x ≠ 0 array cases 0, & x = 0 cases ) then f (x) is… BITSAT 2018 If f(x) = \ cases e^ x , & x ≤ 0 |1 - x|, & x > 0 cases ), then BITSAT 2017 The value of f ( 0 ) , so that the function f(x) = 2x - ^ -1 x 2x + ^ -1 x is continuous… BITSAT 2017 Consider the greatest integer function, defined by f ( x ) = [ x ] , 0 ≤ x < 2 . Then BITSAT 2017 The number of points at which the function f(x)= 1 |x| is discontinuous is: BITSAT 2016 If f(x)=\ array cl x x (1+x^ 2 ) & , x ≠ 0 0 & , x=0 array . then f(x) is BITSAT 2016 If a function f(x) is given by f(x)=(x)/(1+x)+(x)/((x+1)(2 x+1))+(x)/((2 x+1)(3 x+1))+…… BITSAT 2015 Let f: R arrow R be a function such that f(x+y)=f(x)+f(y), x, y ∈ ℝ If f(x) is… BITSAT 2015 Let f(x)=\ array c (x-1) (1)/(x-1) if x ≠ 1 0 if x=1 array . Then which one of the… BITSAT 2014 Let f(x)=\ array l 1- ^ 3 x 3 ^ 2 x , x (π)/(2) array . If f(x) is continuous at… BITSAT 2014 If the function f(x)= cases A x-B, & x ≤ 1 3 x & , 1< x< 2 B x^ 2 -A, & x ≥ 2 cases is… BITSAT 2012 The function f(x)=(x-1) |ℓ n x| is at x=1) BITSAT 2011 The value of | array ccc 1 & 2 & 3 -4 & 3 & 6 2 & -7 & 9 array | is BITSAT 2010 Full Continuity and Differentiability list Continuity and Differentiability JEE Maths PYQs JEE Mathematics PYQs All BITSAT PYQs