Taking the derivative will give you the velocity at any time.
g(x)=4-(x-6)^2
g(x)=4-(x^2-12x+36)
g(x)=4-x^2+12x-36
g(x)=-x^2+12x-32
dg/dx=-2x+12
So g(x) will be increasing when dg/dx>0
-2x+12>0
-2x>-12
x<6
So g(x) is increasing on the interval (-oo, 6)
g(x) will be decreasing when dg/dx<0
-2x+12<0
-2x<-12
x>6
So g(x) will be decreasing on the interval (6, +oo)
