Within-the-interval-0-x-2pi-find-the-critical-points-of-f-x-sin-2-x-sin-x-1-Identify-the-open-interval-on-which-f-is-increasing-and-decreasing-Find-the-function-s-local-and-absolute-extreme-v Tinku Tara June 4, 2023 Differentiation 0 Comments FacebookTweetPin Question Number 123812 by benjo_mathlover last updated on 28/Nov/20 Withintheinterval0⩽x⩽2π,findthecriticalpointsoff(x)=sin2x−sinx−1.Identifytheopenintervalonwhichfisincreasinganddecreasing.Findthefunction′slocalandabsoluteextremevalues. Answered by liberty last updated on 28/Nov/20 Thefunctionfiscontinousover[0,2π]anddifferentiableover(0,2π)sothecriticalpointsoccuratthezerosoff′in(0,2π).Wefindf′(x)=(2sinx−1)cosx.Thefirstderivativeiszeroifonlyifsinx=12orcosx=0.Sothecriticalpointsoffin(0,2π)arex=π6;5π6;π2;3π2theypartition[0,2π]intoopenintervalsasfollowsinterval:(0,π6)(π6,π2)(π2,5π6)(5π6,3π2)(3π2,2π)signoff′:−+−+−behavioroff:decincdecincdecthereisalocalminimumvalueoff(π6)=−54,alocalmaximumvalueoff(π2)=−1,anotherlocalminimumvalueoff(5π6)=−54andanotherlocalmaximumvalueoff(3π2)=1.Theendpointvaluearef(0)=f(2π)=−1.Theabsoluteminimumin[0,2π]is−54occuringatx=π6andx=5π6;theabsolutemaximumis1occuringatx=3π2. Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: lim-x-0-x-1-n-k-1-n-k-x-n-n-Next Next post: Among-all-triangles-in-the-first-quadrant-formed-by-the-x-axis-the-y-axis-and-tangent-lines-to-the-graph-of-y-3x-x-2-what-is-the-smallest-possible-area- Leave a Reply Cancel replyYour email address will not be published.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.