(6x2−42x+36)=12x−42 For maxima\/minima points, f′(x)=0. ⇒6x2−42x+36=0 ⇒x2−7x+6=0 ⇒x2−6x−x+6=0 ⇒x(x−6)−(x−6)=0 ⇒(x−6)(x−1)=0 ⇒x−6=0OR×−1=0 ⇒x=6 OR x=1 Now, let's check these points for maxima\/minima by inspecting the values of f′′(x) at these points. f′(6)=12(6)−42=72−42=30. f′(1)=12(1)−42=12−42=−30. Since, f′(6)=30>0, it is the point of minimum value. And the minimum value is f(6) : =2(6)3−21(6)2+36(6)−20 =432−756+216−20 =−128