01:640:151 Lecture Notes - Lecture 15: Maxima And Minima
Document Summary
Absolute minimum of f on i if f(a) (cid:3409) f(x) for all x l f(a) (cid:3410) f(x) for all x l. Abs min f(c1) (cid:3410) f(x) for all x in 1 f(c2) (cid:3409) f(x) for all x in 2. The extreme value theorem (theorem 1 in sec 4. 2) (e. v. t) A continuous function f on a closed bounded interval l = [a, b] takes on both a min and maximum value on l. Note ( , ) closed not bounded s min a b. F is defines on [a, b] but f is not continuous f(x) = 1x on (0, ) C = if you draw an open interval around c, there will always be some points greater and some small, no matter how small the interval is. c a b. A number c in the domain of f is a critical point (sometimes called a critical number) if either f"(cid:894)c(cid:895) = 0 or f"c does (cid:374)ot exist.
