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JEE Main202315 Apr 2023Morning ShiftMathematicsContinuity and DifferentiabilityActual

Let x denote the greatest integer function and f x = max 1 + x + x , 2 + x , x + 2 x , 0 ≤ x ≤ 2 , where f is not continuous and n be the number of points in 0 , 2 , where f is not differentiable. Then m + n 2 + 2 is equal to

Options

  1. A2
  2. B11
  3. C6
  4. D3

Correct answer

D. 3

Step-by-step solution

Given, f x = max 1 + x + x ,   2 + x ,   x + 2 x ,   0 ≤ x ≤ 2 ⇒ f x = max x + 1 ,   x + 2 ,   x 0 ≤ x < 1 max x + 2 ,   x + 2 ,   x + 2 1 ≤ x < 2 max 5 ,   4 ,   6 x = 2 ⇒ f x = x + 2 , 0 ≤ x < 1 x + 2 , 1 ≤ x < 2 6 , x = 2 ⇒ f ( x ) = x + 2 0 ≤ x < 2 6 x = 2 So, f is not continuous at x = 2 as f 2 - = 4   &   f 2 = 6 And f is differentiable in 0 ,   2 as x + 2 is a linear

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