Consider the polynomial \( f(x)=a x^{2}+b x+c \). If \( f(0)=0 \), ...

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Consider the polynomial \( f(x)=a x^{2}+b x+c \). If \( f(0)=0 \),
P \( f(2)=2 \), then the minimum value of \( \int_{0}^{2}\left|f^{\prime}(x)\right| d x \) is

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