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JEE Main20241 Feb 2024Evening ShiftMathematicsContinuity and DifferentiabilityActual

Let f x = 2 x 2 + 5 x - 3 , x ∈ R . If m and n denote the number of points where f is not continuous and not differentiable respectively, then m + n is equal to:

Options

  1. A5
  2. B2
  3. C0
  4. D3

Correct answer

D. 3

Step-by-step solution

Given: f x = 2 x 2 + 5 x - 3 Now, let y = 2 x 2 + 5 x − 3 ⇒ y = 2 x 2 + 6 x - x − 3 ⇒ y = 2 x x + 3 - x + 3 ⇒ y = 2 x - 1 x + 3 Graph of ⇒ y = 2 x - 1 x + 3 is given below: Graph of f x = 2 x 2 + 5 x - 3 is given below: So, f x is continuous for x ∈ R and non-differentiable at x = ± 1 2 , 0 So, number of points of discontinuity = 0 = m Also, number of points of non-discontinuity = 3 = n ⇒ m + n = 3

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