Which of these functions exhibits a sharp corner in its graph at x = 0, meaning it is not differentiable there? A. x³ B. sin x C. |x| D. cos x Answer: C) |x| Explanation: The absolute value function |x| has a sharp V-shaped corner at x = 0, resulting in differing left and right derivatives (−1 and 1).

imo class 12 continuity and differentiability

Which of these functions exhibits a sharp corner in its graph at x = 0, meaning it is not differentiable there?

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Which of these functions exhibits a sharp corner in its graph at x = 0, meaning it is not differentiable there?

Answer: C) |x|

Explanation: The absolute value function |x| has a sharp V-shaped corner at x = 0, resulting in differing left and right derivatives (−1 and 1).