`g(x) = x^2 - 2x - 8` Identify the open intervals on which the function is increasing or decreasing.
Find the critical values by setting the derivative equal to zero and solving for the x value(s).
The critical value is x=1.
If g'(x)>0 the function will increase over an interval.
If g'(x)<0 the function will decrease over an interval.
Choose an x value less than 1.
g'(0)=-2 Since g'(0)<0 the function will decrease in the interval (-`oo, 1).`
Choose an x value greater than 2.
g'(2)=2 Since g'(2)>0 the function will increase in the interval (1, `oo).`
Because the function changed direction from decreasing to increasing a relative minimum will exist. The relative minimum will occur at the point (1, -9).