Question

Identify intervals on which the function is increasing, decreasing, or constant. g(x) = 4 - (x - 6)^2 ??

Answer 1

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)