Answer
Increasing: $(3,\infty)$
Decreasing: $(-\infty,3)$
Work Step by Step
Everything left of $x=3$ seems to be decreasing and everything to its right is increasing.
We can calculate it by finding the derivative:
$f(x)=x^2-6x+8$
$f'(x)=2x-6$
$0=2x-6$ [Set f'(x) = 0 to find critical values]
$x=3$
Test values greater than 3 and less than 3:
$f'(4)=2(4)-6$
$f'(4)=2>0$
Therefore all numbers greater than 3 is increasing.
$f'(2)=2(2)-6$
$f'(2)=-2<0$
Therefore all numbers less than 3 is decreasing.
