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BITSAT2017MathematicsContinuity and DifferentiabilityActual

If f x = e x , x ≤ 0 1 - x , x > 0 , then

Options

  1. Af x is differentiable at x = 0
  2. Bf x is continuous at x = 0 , 1
  3. Cf x is differentiable at x = 1
  4. DNone of the above

Correct answer

B. f x is continuous at x = 0 , 1

Step-by-step solution

f x = e x , x ≤ 0 1 - x , 0 < x ≤ 1 x - 1 , x > 1 R H D :   f ' 0 = lim h → 0 f 0 + h - f 0 h = lim h → 0 - h - 1 h = - 1 L H D :   f ' 0 = lim h → 0 f 0 - h - f 0 - h = lim h → 0 e - h - 1 - h = 1 So, it is not differentiable at x = 0 . Similarly, it is not differentiable at x = 1 but it is continuous at x = 0 and 1 .

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