Identify the function's local and absolute extreme values, if any, saying where they occur.

$g(x)=\frac{4}{4}+\frac{4}{3}{x}^3-\frac{2}{2}{x}^2-36x+2$

local maximum at $x=-3$; local minima at $x=-4$ and $x=3$

local maximum at $x=-4$; local minimum at $x=3$

local maxima at $x=-4$ and $x=3$; local minimum at $x=-3$

local maxima at $x=4$ and $x=-3$; local minimum at $x=-3$