let-f-x-x-3-x-1-1-prove-that-1-2-f-0-2-use-the-newton-method-with-x-0-3-2-to-find-a-better-value-for-take-onlly-5-terms- Tinku Tara June 4, 2023 Relation and Functions 0 Comments FacebookTweetPin Question Number 40407 by prof Abdo imad last updated on 21/Jul/18 letf(x)=x3−x−11)provethat∃α∈]1,2[/f(α)=02)usethenewtonmethodwithx0=32tofindabettervalueforα(takeonlly5terms) Answered by maxmathsup by imad last updated on 25/Jul/18 1)wehavef′(x)=3x2−1>0oninterval]1,2[soisincreasingon]1,2[f(1)=1−1−1=−1andf(2)=8−3=5⇒f(1).f(2)<0⇒∃!α∈]1,2[/f(α)=02)wehavex0=32andxn+1=xn−f(xn)f′(xn)⇒x1=x0−f(xo)f′(x0)=32−f(32)f′(32)butf(32)=(32)3−32−1=278−52=27−208=78f′(32)=3(32)2−1=274−1=234⇒x1=32−78234=32−78.423=32−746=138−1492=12492=6246=3123x2=x1−f(x1)f′(x1)=3123−f(3123)f′(3123)…..becontinued… Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Question-40406Next Next post: Question-105945 Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.