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The function \( f(x) = x^3 - 3x^2 + 4 \) has a local minimum at \( x = a \). Find the value of \( a \).
First, find the derivative: \( f'(x) = 3x^2 - 6x \).
Set \( f'(x) = 0 \) to find critical points: \( 3x(x - 2) = 0 \).

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