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

• A

  $(-6,11)$
• B

  $(2 - \frac{1}{\sqrt{3}},2 + \frac{1}{\sqrt{3}})$
• Correct answer
  C

  $(11,-6)$
• D

  $(6,11)$

Hence, the correct answer is option: 'C'.