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JEE Main201910 Jan 2019Morning ShiftMathematicsContinuity and DifferentiabilityActual

Let f x = m a x x , x 2 , x ≤ 2 8 - 2 x , 2 < x ≤ 4 . Let S be the set of points in the interval - 4 , 4 at which f is not differentiable. Then S

Options

  1. Aequals - 2 ,   - 1 ,   0 ,   1 ,   2
  2. Bequals - 2 ,   2
  3. Cis an empty set
  4. Dequal - 2 ,   - 1 ,   1 ,   2

Correct answer

A. equals - 2 ,   - 1 ,   0 ,   1 ,   2

Step-by-step solution

Given function is f x = m a x x ,   x 2 , x ≤ 2 8 - 2 x , 2 < x ≤ 4 The graph of the function, is We know that, a function is not differentiable at a point where its graph has a sharp corner. And, from the graph we can easily conclude that f x is non-derivable at x = - 2 ,   - 1 ,   0 , 1 ,   2 Hence, the set S = - 2 ,   - 1 ,   0 , 1 ,   2 .

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