What is difference between critical points and inflection points?

1 Answer
May 18, 2015

In the textbook I use (Stewart Calculus)

critical point of #f# = critical number for #f# = value of #x# (the independent variable) that is 1) in the domain of #f#, where #f'# is either #0# or does not exists. (Values of #x# that meet the conditions of Fermat's Theorem.)

An inflection point for #f# is a point on the graph (has both #x# and #y# coordinates) at which the concavity changes.

(Other people seem to use other terminology. I don't know f they ate mistaken or just have different terminology.. But the textbooks I've used in the U.S since the early 80s have all used this definition.)