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

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

x = $\displaystyle \frac{1}{\sqrt{3}} $

The question says if the function $\displaystyle f(x) = x^3+ax^2+bx $ has a local min of $\displaystyle \frac{-2}{9}\sqrt{3} $ at x = $\displaystyle \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!!