At how many points in is the function not differentiable?
Answer and explanation
Correct answer: A.
- Step 1: The absolute value function is continuous everywhere on , but has a sharp corner (cusp) and is non-differentiable at .
- Step 2: The function is linear in each of the intervals , , and .
- 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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