Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main201911 Jan 2019Evening ShiftMathematicsContinuity and DifferentiabilityActual

Let K be the set of all real values of x where the function f(x)= |x|-|x|+2(x- ) |x| is not differentiable. Then the set K is equal to :

Options

  1. A(an empty set)
  2. B(
  3. C0
  4. D0,

Correct answer

A. (an empty set)

Step-by-step solution

f(x)= |x|-|x|+2(x- ) |x| There are two cases, Case (1), x>0f(x)= x-x+2(x- ) xf^ (x)= x-1+2(1-0) x-2 (x- )f^ (x)=3 x-2(x- ) x-1 Then, function f(x) is differentiable for all x>0 Case (2) x < 0f(x)=- x+x+2(x- ) xf^ (x)=- x+1-2(x- ) x+2 xf^ (x)= x+1-2(x- ) x Then, function f(x) is differentiable for all x < 0 Now check for x=0f^ (0^ * ) R HD =3-1=2f^ (0) L . H.D. =1+1=2 L . HD = R . H.D Then, function f(x) is differentiable for x=0 . So it is differentiable everywhere Hence, k=

Practice Continuity and Differentiability on Quantrex Academy →

More from Continuity and Differentiability

Let R denote the set of all real numbers. Let f : R R be an arbitrary function and let g : R R be the function defined by g(x) = x f(x) , for all x R . Then which of the following 2026Consider the function f : (- 2 , 2 ) (- , ) defined by f(x) = (|x| + |x - 1|) x + [x x] , where [x x] is the greatest integer less than or equal to x x . Let be the total number of 2026For a real number , let [ ] denote the greatest integer less than or equal to . For a finite set S , let |S| denote the number of elements in the set S . Consider the functions f : 2026For the function f(x) = e^ |x| - |x| , x R , consider the following statements: Statement I: f is differentiable for all x R . Statement II: f is increasing in (- , - 2 ) . In the 2026Let f(x) = cases 1 3 , & x /2 b(1- x) ( -2x)^2 , & x > /2 cases . If f is continuous at x= /2 , then the value of ₀^ 3b-6 |x^2+2x-3| ,dx is: 2026Let f(x) = cases x^3 + 8 ; & x Then the number of points, where the function g f is discontinuous, is __________. 2026Let f(x)= cases e^ x-1 , & x<0 x^2-5x+6, & x 0 cases and g(x)=f(|x|)+|f(x)| . If the number of points where g is not continuous and is not differentiable are and respectively, then 2026The number of points, at which the function f(x) = 6x, 2 + 3x^2 + |x - 1| | |x^2 - 1 4 | | , x (- , ) , is not differentiable, is _____. 2026 Full Continuity and Differentiability list All JEE Main PYQs