x squared minus four, at which intervals is the function increasing or decreasing?

Answer 1

if f '( x ) > 0 then f is increasing

if f '( x ) < 0then f is decreasing

In this case:

f ( x ) = x ^ 2 - 4

f '( x ) = 2 x

f '( x ) < 0 on interval (-infinity , 0 ]

f '( x ) > 0 on interval [ 0 , infinity ]