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Calculus
Continuity and Differentiability, Absolute Value Functions
jee_adv_2026_mock_p2
Grade 12
Question:
Let f(x) = |x^3 - 6x^2 + 11x - 6|. The number of points where f(x) is non-differentiable is:
A. 1
B. 2
C. 3
D. 4
Step-by-Step Solution
Key Concept: Non-differentiability occurs at points where the expression inside the absolute value changes sign.
Step 1: x^3 - 6x^2 + 11x - 6 = (x-1)(x-2)(x-3). Step 2: The points of non-differentiability occur at the roots: x = 1, 2, 3. Step 3: At each point, the left and right derivatives differ. Step 4: Hence total points = 3.
Correct Answer:C
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