The function $f(x)=\frac{1}{12}(3x^4+4x^3-12x^2)$ decreases in

$(-∞,-2) ∪ (0, 1)$

$f(x)=\frac{1}{12}(3x^4+4x^3-12x^2)$

$f(x)$ decreases when $g(x) = 3x^4+4x^3-12x^2$ decreases.

differentiating g(x) w.r.t x

$g'(x)=12x^3+12x^2-24x$

$=12x(x^2+x-2)$

$=12x(x^2+2x-x-2)$

$=12x(x(x+2)-1(x+2))$

$=12x(x-1)(x+2)$

$g'(x)=0$ for $x = -2,0,1$

g(x) and f(x) are decreasing in 

$(-∞,-2) ∪ (0, 1)$