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Consider f x = - 2 , - 2 ≤ x < 0 x 2 - 2 , 0 ≤ x ≤ 2 and g x = f x + f x . Then, in the interval - 2 , 2 ,   g x is

Options

  1. Anot differentiable at one point
  2. Bdifferentiable at all points
  3. Cnot continuous
  4. Dnot differentiable at two points

Correct answer

A. not differentiable at one point

Step-by-step solution

Given, f x = - 2 , - 2 ≤ x < 0 x 2 - 2 , 0 ≤ x ≤ 2 ∴ f x = 2 , - 2 ≤ x < 0 2 - x 2 ,     0 ≤ x < 2 x 2 - 2 , 2 ≤ x ≤ 2 And f x = x 2 - 2 ,   x ∈ - 2,2 ∴ g x = x 2 , - 2 ≤ x < 0 0 , 0 ≤ x < 2 2 x 2 - 2 , 2 ≤ x ≤ 2 g ′ x = 2 x − 2 < x < 0 0 0 < x < 2 4 x 2 < x < 2 g ' 0 − = 0 = g ' 0 + g ' 2 − = 0 , g ' 2 + = 4 2 So, g x is not differentiable at x = 2

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