If \( f(x)=x^{3}+x^{2} f^{\prime}(1)+x f^{\prime \prime}(2)+f^{\prime \prime \prime}(3) \) for a....

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If \( f(x)=x^{3}+x^{2} f^{\prime}(1)+x f^{\prime \prime}(2)+f^{\prime \prime \prime}(3) \) for all real \( x \),
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then
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(1) \( f^{\prime}(1)=-5 \)
(2) \( f^{\prime \prime}(2)=2 \)
(3) \( f^{\prime \prime \prime}(3)=6 \)
(4) \( f(0)=6 \)


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