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Most Important Selected Qs for JEE AdvancedMathematicsContinuity and Differentiability

If function f(x)= cases |x-2| & x 1 x^2 5 - 4 x 5 + 8 5 & ; x 1 cases

Options

  1. Acontinuous at x=1
  2. Bdifferentiable at x=1
  3. Cnot differentiable at x=1
  4. Ddifferentiable at x=2

Correct answer

C. not differentiable at x=1

Step-by-step solution

Redefining the function, we get f(x)= array cc x^2 5 - 4 x 5 + 8 5 ; & x 1 2-x & ; x [1,2) x-2 & ; x 2 array . We have R.H.L at x=1 is = _ h 0 2-(1+h)=1 L.H.L at x=1 is = _ h 0 (1-h)^2 5 - 4(1-h) 5 + 8 5 =1 f ( x ) is continuous at x =1 Now f^ (x)= array cc 2 x 5 - 4 5 & ; x 1 -1 & ; 1 x 2 1 ; & x 2 array . R.H.D at x=1 -1 L.H.D at x=1 - 2 5 Not differentiable at x =1 Not differentiable at x=2

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