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If f x = m i n 9 - x 2 , 1 + x 2 , ∀ x ∈ - 3,3 , then the number of point(s) where f x is non-differentiable is/are

Options

  1. A4
  2. B3
  3. C2
  4. D0

Correct answer

A. 4

Step-by-step solution

Using graph of y = 9 - x 2 ⇒ x 2 + y 2 = 9 , y = 1 + x 2 ⇒ y 2 - x 2 = 1 In the figure, we can see the graph of f x Clearly, f x is non-differentiable at x = - 3 ,   x 1 ,   x 2 ,   3 ( 4 points) because there are sharp points at x 1 ,   x 2 and at x = 3 , x = – 3 there are vertical tangents.

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