MATH 140 Lecture 17: Derivative Tests
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Hf isdiffon a b thereissavevalue x c incabist tcbi. fi a. Picture intuition theavgrate of change insrateof change somepoint i a c o whatis tcb flag. Findwhere t is p and d film 123122 2411. 12 1 211 1 crit s x o 1,2 thesedividethedomain intointervals localmin x 1,2 localmax x o d is a if. Neg g is inc f o f co gisdec t o f isinc. Ex find thelocalextrema of f x x 28in x on 0,21t. 511 2 3 canneverbezero includepointsthatmake unaeoned it no tmofmthxh. Is s f is in localmin ti isdec o. X 4iz x 21t second deriv test secondderivisthederivofthederiv f fi. Therelationshipbetween flandf isexactly isexactlythe relationship between a functionanditsderiv. Iii fifi iiincreasingmen. ms angen ne. a. eg ocoo iteimt iiiiiimii. i. ms. Recallcriticalptfor f is an value x c satisfying. 2 5 c 0 or f c one. If thesignof f changes across a2ndcritpt getan inflectionpt concaneup aif int concave down ex discussfix xt 43 intermsof1stand2nd.
