At how many points in is the function not differentiable?

Answer and explanation

Correct answer: A.

  1. Step 1: The absolute value function is continuous everywhere on , but has a sharp corner (cusp) and is non-differentiable at .
  2. Step 2: The function is linear in each of the intervals , , and .
  3. Step 3: The sharp corners occur at the critical transition points and , where the left and right derivatives differ. Thus, is not differentiable at exactly points.
Answer
.
Why not the others: counts only one of the corner points; counts an extra non-existent point between and ; assumes continuity implies differentiability.

Practise more Limits, continuity and differentiability.

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