The number of points where $f(x) = |2x + 1| - 3|x + 2| + |x^2 - x - 2|$ is not differentiable is:
Step-by-Step Solution
Key Concept: Find where each absolute value changes sign: $2x+ 1 = 0 \Rightarrow x = -1/2$; $x+ 2 = 0 \Rightarrow x = -2$; $x^2 - x - 2 = (x - 2)(x + 1) = 0 \Rightarrow x = 2, -1$. Critical points: $\{-2, -1, -1/2, 2\}$ — but simplify $f$ on each interval and check corners. Two non-differentiable points remain.
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Correct Answer: (3)