$\text{ If }c\text{ is a point at which Rolle's theorem holds for the function, }\mathrm{f}\left(\mathrm{x}\right)={\log }_{\mathrm{e}}\left(\frac{{\mathrm{x}}^2+\alpha }{7\mathrm{x}}\right)\text{ in }$

$\text{ the interval }[3,4],\text{ where }\alpha \in \mathrm{R},\text{ then }{\mathrm{f}}^{\text{'}\text{'}}\left(\mathrm{c}\right)\text{ is equal to: }$

• A

  $\frac{\sqrt{3}}{7}$

• B

  $-\frac{1}{12}$

• C

  $-\frac{1}{24}$

• D

  $\frac{1}{12}$