MATH 121 Lecture Notes - Lecture 17: Maxima And Minima, Stationary Point
Document Summary
Suppose a function f has a derivative at each point in an open interval; then if. > 0 for each x in the interval, f is increasing on the interval; f. < 0 for each x in the interval, f is decreasing on the interval. A stationary point is where the rate of change (derivative) of function. Furthermore, f(c) is a relative (or local) minimum for f if there exists an open interval (a, b) containing c such that f (x) f (c) for all x in (a, b). is zero. Note: the at part is the x-value and the of part is the y-value. Absolute extrema: has an absolute maximum at = if (cid:4666)(cid:4667)(cid:3410)(cid:4666)(cid:4667) for every in the domain of . has an absolute minimum at = if (cid:4666)(cid:4667)(cid:3409)(cid:4666)(cid:4667) for every in the domain of . Example 1: find the absolute max. or absolute min. from the graphs below.
