`f(x) = x^2 - 4x` Find the critical numbers, open intervals on which the function is increasing or decreasing, apply first derivative test to identify all relative extrema.
Find the critical values of x by setting the derivative of the function equal to zero and solving for the x-value(s).
The critical value is at x=2.
If f'(x)>0, then the function is increasing on that interval.
If f'(x)<0, then the function is decreasing on that interval.
Choose any value for x that is less than 2.
Since f'(0)<0, the function is decreasing on the interval `(-oo, 2).`
Choose any value for x that is greater than 2.
Since f'(3)>0, then the function is increasing on the interval (2, `oo).`
Since the sign of the derivative changed from negative to positive, then there will absolute minimum at x=2. The absolute minimum is the point (2, -4).