Let f(x) = |x^3 - 3x^2 + 2x| + |x^2 - 4x + 3|. The number of points in (-∞, ∞) where f(x) is non-differentiable is:
Step-by-Step Solution
Key Concept: Non-differentiability occurs at points where expressions inside absolute values change sign.
Step 1: Factor x^3 - 3x^2 + 2x = x(x-1)(x-2), giving critical points 0, 1, 2. Step 2: Factor x^2 - 4x + 3 = (x-1)(x-3), giving critical points 1, 3. Step 3: Union of critical points is {0, 1, 2, 3}. Step 4: At each point, the left and right derivatives differ. Hence total points = 4.
Correct Answer: B