This is one of the the things I did not quite master in my calculus 1 course last semester. I understand for a function to be different on a point a. It must be defined at point a n not have any cusp or appear vertically tangent. My question is for a general function. How to I sketch it's derivative? What I do know: horizontal tangents are very important because these points will lie on the x-axis. Pay attention to see where the line is decreasing and increasing. Do not understand what to do with the increasing and decreasing portion. My book Stewart does not really explain this portion of derivatives in terms I can understand. Sorry for this elementary question.