MATH116 Lecture Notes - Lecture 4: Asymptote, Eaves, Cartesian Coordinate System
9 Dec 2015
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Friday, october 30 lecture 19 : derivatives and the shape of a graph. (refers to. Students who have mastered the content of this lecture know about: the first derivative test, concavity, what defines concave upwards and concave downward, inflection points, the second derivative test. Introduction we have seen how the derivative along with the increase-decrease theorem, can help us determine on which intervals a function f is increasing and decreasing. Note that a local maximum or minimum may be an endpoint . So an endpoint is always considered as possible local extremum. An absolute maximum and absolute minimum are by definition local extrema. It may also be on a part of the curve where there is not derivative: consider the curve of f (x) = | x | at x = 0 for example. The first graphing tool is called the first derivative test. It is an immediate consequence of the increase-decrease theorem.
