Reading the Derivative’s Graph

A very typical calculus problem is given the equation of a function, to find information about it (extreme values, concavity, increasing, decreasing, etc., etc.). This is usually done by computing and analyzing the first derivative and the second derivative. All the textbooks show how to do this with copious examples and exercises. I have nothing…

Good Question 17

A common question in (older?) textbooks is to give students a function or relation and have them graph it without technology (because in the old days technology was not available). Students had to find all the appropriate information without hints or further direction: they were supposed to know what to do and do it. AP…

Asymptotes and the Derivative

What does an asymptote of the derivative tell you about the function? How do asymptotes of a function appear in the graph of the derivative? One of my most read posts is Reading the Derivative’s Graph, first published seven years ago. The long title is “Here’s the graph of the derivative; tell me about the…