Find the derivative function (f'(x))
Identify critical points where (f'(x)=0) or (f'(x)) is undefined
Determine intervals where (f'(x)>0) and (f'(x)<0)
Plot the derivative values for several (x)-values
Mark zeros of (f'(x)) on the graph
Use sign changes to show where the original function increases or decreases
Check for local maxima and minima of the original function at zeros of (f'(x))
Identify points where (f'(x)) changes from positive to negative or negative to positive
Graph the slope behavior as (x) changes
If needed, use the second derivative (f”(x)) to locate concavity changes in (f'(x))
Connect plotted points smoothly when the derivative is continuous
Leave breaks or open circles where the derivative is undefined