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If $f$ is defined in $[1,3]$ by $f(x)=x^3+b x^2+a x$, such that $f(1)-f(3)=0$ and $f^{\prime}(\mathrm{c})=0$, where $c=2+\frac{1}{\sqrt{3}}$, then $(a, b)$ is equal to
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The correct answer is:
$(11,-6)$
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