If the function
\[
f(x)=x^3+bx^2+ax
\]
satisfies the conditions of Rolle's theorem in \([1,3]\) with
\[
c=2+\frac{1}{\sqrt3},
\]
then \((a,b)=\)
Show Hint
For Rolle's theorem problems, always use the two conditions:
\[
f(a)=f(b)
\]
and
\[
f'(c)=0.
\]
These usually provide enough equations to determine the unknown constants.