find the values of a and b given local minimum value and x

$f(x) = x^3+ax^2+bx$

local min = $\frac{-2}{9}\sqrt{3}$
x = $\frac{1}{\sqrt{3}}$

The question says if the function $f(x) = x^3+ax^2+bx$ has a local min of $\frac{-2}{9}\sqrt{3}$ at x = $\frac{1}{\sqrt{3}}$ what are the values of a and b?

b). which of the tangent lines to the curve in part a has the smallest slope?

Please lead me in the right way i dont care about the answers just tell me how i would find the values a or b
i tried plugging in the value of x into f(X) Then i found the derivative and i got stuck
thanks!!