COMEDK20269 May 2026Evening ShiftMathematicsContinuity and DifferentiabilityActual
The function f(x) = |x| + |x - 1| is:
Options
- ADifferentiable at x = 1 but not at x = 0
- BNeither differentiable at x = 0 nor x = 1
- CDifferentiable at x = 0 and x = 1
- DDifferentiable at x = 0 but not at x = 1
Correct answer
B. Neither differentiable at x = 0 nor x = 1
Step-by-step solution
The given function is f(x) = |x| + |x - 1| . We can redefine the function as a piecewise function: f(x) = cases -x - (x - 1) = -2x + 1, & x Checking differentiability at x = 0 : Left Hand Derivative (LHD) = _ x 0^- f'(x) = -2 Right Hand Derivative (RHD) = _ x 0^+ f'(x) = 0 Since LHD RHD, f(x) is not differentiable at x = 0 . Checking differentiability at x = 1 : Left Hand Derivative (LHD) = _ x 1^- f'(x) = 0 Right Hand Derivative (RHD) = _ x 1^+ f'(x) = 2 Since LHD RHD, f(x) is not differentiable at x = 1 . Therefo