Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main2015MathematicsContinuity and DifferentiabilityActual

If the function g x = k x + 1 , 0 ≤ x ≤ 3 m x + 2 , 3 < x ≤ 5 is differentiable, then the value of k + m is

Options

  1. A4
  2. B2
  3. C16 5
  4. D10 3

Correct answer

B. 2

Step-by-step solution

LHD at x = 3 lim x ⟶ 3 - ⁡ k x + 1 - 2 k x - 3 =   lim x → 3 - ⁡k x - 3 x - 3 . 1 x + 1 + 2 = k 4 RHD at x = 3 lim x → 3 + ⁡ m x + 2 - 2 k x - 3 Since this limit exists if 3 m + 2 - 2 k = 0   . . . i ( 0 0 form) So, lim x → 3 + ⁡ m x + 2 - 3 m + 2 x - 3 = m Hence m = k 4   … ii From i   &   ii m = 2 5   &   k = 8 5     ⇒ k + m = 2

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