If f(x)=a| x|+b e^ |x| +c|x|^3 , where a, b, c ∈ R , is differentiable at x=0 , then

Correct answer: D. a=0, b=0, c is any real number | x| and e^ |x| are not differentiable at x=0 and |x|^3 is differentiable at x=0 . for f(x) to be differentiable at x=0 , we must have a=0, b=0 and c is any real number.

JEE Main 201226 MayOnline

Exam: JEE Main
Year: 2012
Date: 26 May
Mode: Online
Subject: Mathematics
Chapter: Continuity and Differentiability

JEE Main 2012 · 26 May · Online · Mathematics · Continuity and Differentiability

If f(x)=a| x|+b e^ |x| +c|x|^3 , where a, b, c ∈ R , is...

f(x)=a|\sin x|+b e^{|x|}+c|x|^3

, where

a, b, c \in R

, is differentiable at

x=0

, then

Options

A $a=0, b$ and $c$ are any real numbers
B $c=0, a=0, b$ is any real number
C $b=0, c=0, a$ is any real number
D $a=0, b=0, c$ is any real number

Correct answer

D. $a=0, b=0, c$ is any real number

Step-by-step solution

|\sin x|

and

e^{|x|}

are not differentiable at

x=0

and

|x|^3

is differentiable at

x=0

\therefore

for

f(x)

to be differentiable at

x=0

, we must have

a=0, b=0

and

c

is any real number.

Practice Continuity and Differentiability on Quantrex Academy →

More from Continuity and Differentiability

Let ℝ denote the set of all real numbers. Let f : ℝ arrow ℝ be an arbitrary function and… JEE Advanced 2026 Consider the function f : (-(π)/(2), (π)/(2)) arrow (-∞, ∞) defined by f(x) = (|x| + |x… JEE Advanced 2026 For a real number α , let [α] denote the greatest integer less than or equal to α . For a… JEE Advanced 2026 For the function f(x) = e^ |x| - |x| , x ∈ ℝ , consider the following statements… JEE Main 2026 Let f(x) = cases (1)/(3), & x ≤ π/2 (b(1- x))/((π-2x)^2), & x > π/2 cases . If f is… JEE Main 2026 Let f(x) = cases x^3 + 8 ; & x Then the number of points, where the function g ∘ f is… JEE Main 2026 Let f(x)= cases e^ x-1 , & x<0 x^2-5x+6, & x ≥ 0 cases and g(x)=f(|x|)+|f(x)| . If the… JEE Main 2026 The number of points, at which the function f(x) = \ 6x, 2 + 3x^2\ + |x - 1|| |x^2… JEE Main 2026 The number of points in the interval [2, 4] , at which the function f(x) = [x^2 - x… JEE Main 2026 Let f(x)= _ θ arrow 0 ( π x-x^ ((2)/(θ)) (x-1) 1+x^ ((2)/(θ)) (x-1) ), x ∈ R . Consider… JEE Main 2026 Let [t] denote the greatest integer less than or equal to t . If the function f(x)=\… JEE Main 2026 If the function f(x)= e^ x (e^ x-x -1)+ _ e ( x+ x)-x x-x is continuous at x=0 , then the… JEE Main 2026 Let α, β ∈ ℝ be such that the function f(x)= cases 2 α(x^ 2 -2)+2 β x &, x be… JEE Main 2026 If f(x)=\ array cc a|x|+x^ 2 -2( |x|)( |x|) x &, x ≠ 0 b &, x=0 array . is continuous at… JEE Main 2026 Let f(x)= cases a x^ 2 +2 a x+3 4 x^ 2 +4 x-3 &, x ≠-(3)/(2), (1)/(2) ~b &, x=-(3)/(2)… JEE Main 2026 Let [·] denote the greatest integer function, and let f(x)= \ 2 x, x^ 2 \ . Let S = \ x… JEE Main 2026 Full Continuity and Differentiability list Continuity and Differentiability JEE Maths PYQs JEE Mathematics PYQs All JEE Main PYQs