The number of points of local extrema of $f(x) = 2x^3 - 15x^2 + 36x + 1$ equals _____.
Step-by-Step Solution
Key Concept: Solve $f'(x) = 0$ to find the critical points, then verify using a sign change of $f'$ (or $f''$) around each one that it is a genuine local extremum, not an inflection point.
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Correct Answer: 2