AP EAMCET201823 Apr 2018Morning ShiftMathematicsContinuity and DifferentiabilityActual
Let f be defined on D=[R- -1,1 by f(x)= |x| 1-|x| , then
Options
- Af is differentiable on D
- Bf is differentiable on D except at x = 0
- Cf is continuous but not differentiable on D
- Df is differentiable but not continuous on D
Correct answer
B. f is differentiable on D except at x = 0
Step-by-step solution
aligned & We have, f(x)= |x| 1-|x| = array l -x 1+x , x < 0 x 1-x , x 0 array . & LHD ( at x=0)= _ h 0 f(0-h)-f(0) -h & = _ h 0 f(-h)-0 -h = _ h 0 h 1-h -h & = _ h 0 -1 1-h =-1 & RHD ( at x=0)= _ h 0 f(0+h)-f(0) h & = _ h 0 f(h)-0 h = _ h 0 h 1-h aligned So, f(x) is not differentiable at x=0 . Hence, f(x) is differentiable on D except at x=0 .