M 427L Lecture Notes - Lecture 19: Second Order (Religious), Reamer, Maxima And Minima

• School: UT-Austin
• Department: Mathematics
• Course: M 427L
• Professor: Theresa Martines

Document Summary

Taylor"s theorem gives an approximation of fcx near a point a f x _f ca t f a ix a a x a f. If d xk aa f x xz. xz f i ffa7tfx. la lxi a tfxrlci1lxza2tfxscaxx a. Ei let f x xz xze tcosh xz findthefirst order taylor approx fine x sina. xdfx. ix. gg x. sincx. x ft. Fci t 2 fx. ci final f f x 1,01 1. 1st partials f x xz f ucr dir f i f a tfx. cakxia. jtfx. dkh. a. jtt2lfiicakxiakxiailt2xiecavk. a. kxz. ae. Find the quad approx for flay e t at thepoint 0,0. It 01 01 1 y o f x. I 124071 0 1 icyoxy o tocx oxyo tocy oscx. at. 3. 3 extreme values for f x y we were. Recall horizontal tangent line www. a. am looking for points with a eonie m i horizontal tangent planes let f ucr. For a an open disk in an opendisk centere. Iii feel la b ca. b f a b is a local minimum reamer can.