Identify where the original graph is increasing, decreasing, or flat
Mark where the original graph has horizontal tangents; the derivative is 0 there
Find where the original graph is steepest upward; the derivative is largest positive there
Find where the original graph is steepest downward; the derivative is most negative there
Locate local maxima and minima of the original graph; the derivative crosses 0 at those x-values
Check for corners, cusps, vertical tangents, or discontinuities; the derivative is undefined there
Use the slope of the original graph at several x-values to estimate derivative values
Plot the estimated derivative points on a new set of axes
Connect the derivative points smoothly where the original graph is smooth
Keep the derivative positive where the original graph rises
Keep the derivative negative where the original graph falls
Keep the derivative near 0 where the original graph is nearly flat
Reflect sharp changes in slope as sharp changes in the derivative graph
Match intervals of constant slope on the original graph with horizontal segments on the derivative graph