The first derivative test is making a “sign diagram” via number line with the increasing/decreasing sketches to determine the nature of the extrema’s:
relative if (-)->(+) or (+)->(-)
no extrema if (-)->(-) or (+)->(+)
Relative Extrema, Local Maximum and Minimum, First Derivative Test, Critical Points (cr: Organic Chemistry Tutor)
First Derivative Test (cr: The Organic Chemistry Tutor)