Ứng dụng đạo hàm để giải quyết một số vấn đề liên quan đến thực tiễn

Home Lớp 12 Toán lớp 12 - Sách Kết nối tri thức Bài 5. Ứng dụng đạo hàm để giải quyết một số vấn đề liên quan đến thực tiễn.Bài tập cơ bản

{"common":{"save":0,"post_id":"7545","level":1,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5472","post_id":"7545","mon_id":"1159285","chapter_id":"1159288","question":"M\u1ed9t ch\u1ea5t \u0111i\u1ec3m chuy\u1ec3n \u0111\u1ed9ng theo ph\u01b0\u01a1ng trình $s(t)=t^2$<\/span>, trong \u0111ó t > 0, t tính b\u1eb1ng giây và $s(t)$<\/span> tính b\u1eb1ng mét. Tính v\u1eadn t\u1ed1c c\u1ee7a ch\u1ea5t \u0111i\u1ec3m t\u1ea1i th\u1eddi \u0111i\u1ec3m t = 2 giây.<\/p>","options":["A.<\/strong> 2m\/s.","B.<\/strong> 3m\/s.","C.<\/strong> 4m\/s.","D.<\/strong> 5m\/s."],"correct":"3","level":"1","hint":"S\u1eed d\u1ee5ng ý ngh\u0129a c\u01a1 h\u1ecdc c\u1ee7a \u0111\u1ea1o hàm v\u1eadn t\u1ed1c c\u1ee7a ch\u1ea5t \u0111i\u1ec3m $v(t)=s^\\prime(t)$<\/span>.<\/p>","answer":"Ch\u1ecdn C.<\/strong> 4m\/s.<\/span><\/p>Ta tính \u0111\u01b0\u1ee3c $s^\\prime(t)=2t$<\/span>.<\/p>V\u1eadn t\u1ed1c c\u1ee7a ch\u1ea5t \u0111i\u1ec3m $v(t)=s^\\prime(t)=2t$<\/span> ⇒ $v(2)=2.2=4$<\/span> m\/s.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-08-04 01:22:48","option_type":"txt","len":0},{"id":"5473","post_id":"7545","mon_id":"1159285","chapter_id":"1159288","question":"M\u1ed9t viên \u0111\u1ea1n \u0111\u01b0\u1ee3c b\u1eafn lên cao theo ph\u01b0\u01a1ng trình $s(t)=196t-4,9t^2$<\/span> trong \u0111ó t  > 0, t tính b\u1eb1ng giây k\u1ec3 t\u1eeb th\u1eddi \u0111i\u1ec3m viên \u0111\u1ea1n \u0111\u01b0\u1ee3c b\u1eafn lên cao và $s(t)$<\/span> là kho\u1ea3ng cách c\u1ee7a viên \u0111\u1ea1n so v\u1edbi m\u1eb7t \u0111\u1ea5t \u0111\u01b0\u1ee3c tính b\u1eb1ng mét. T\u1ea1i th\u1eddi \u0111i\u1ec3m v\u1eadn t\u1ed1c c\u1ee7a viên \u0111\u1ea1n b\u1eb1ng 0 thì viên \u0111\u1ea1n cách m\u1eb7t \u0111\u1ea5t bao nhiêu mét?<\/span><\/p>","options":["A.<\/strong> 1690 m","B.<\/strong> 1069 m","C.<\/strong> 1906 m","D.<\/strong> 1960 m"],"correct":"4","level":"1","hint":"S\u1eed d\u1ee5ng ý ngh\u0129a c\u01a1 h\u1ecdc c\u1ee7a \u0111\u1ea1o hàm v\u1eadn t\u1ed1c c\u1ee7a ch\u1ea5t \u0111i\u1ec3m $v(t)=s^\\prime(t)$<\/span>.<\/p>","answer":"Ch\u1ecdn D.<\/strong> 1960 m<\/span><\/p>Ta tính \u0111\u01b0\u1ee3c $s^\\prime(t)=196-9,8t$<\/span>.<\/p>V\u1eadn t\u1ed1c c\u1ee7a viên \u0111\u1ea1n $v(t)=s^\\prime(t)=196-9,8t$<\/span> <\/p>⇒ $v(t)=0$<\/span> ⇔ $196-9,8t=0$<\/span> ⇔ t = 20.<\/p>Khi \u0111ó viên \u0111\u1ea1n cách m\u1eb7t \u0111\u1ea5t m\u1ed9t kho\u1ea3ng $h=s(20)=196.20-4,9.20^2=1960$<\/span> m.<\/p>","type":"choose","extra_type":"shape2","user_id":"131","test":"0","date":"2024-08-04 01:24:59","option_type":"txt","len":0},{"id":"5475","post_id":"7545","mon_id":"1159285","chapter_id":"1159288","question":"M\u1ed9t ch\u1ea5t \u0111i\u1ec3m chuy\u1ec3n \u0111\u1ed9ng có ph\u01b0\u01a1ng trình $s(t)=t^3-3t^2+9t+2$<\/span>, trong \u0111ó t > 0, t tính b\u1eb1ng giây và $s(t)$<\/span> tính b\u1eb1ng mét. H\u1ecfi t\u1ea1i th\u1eddi \u0111i\u1ec3m nào thì v\u1eadn t\u1ed1c c\u1ee7a v\u1eadt \u0111\u1ea1t giá tr\u1ecb nh\u1ecf nh\u1ea5t?<\/p>","options":["A.<\/strong> t = 1s","B.<\/strong> t = 2s","C.<\/strong> t = 3s","D.<\/strong> t = 6s"],"correct":"1","level":"1","hint":"S\u1eed d\u1ee5ng ý ngh\u0129a c\u01a1 h\u1ecdc c\u1ee7a \u0111\u1ea1o hàm v\u1eadn t\u1ed1c c\u1ee7a ch\u1ea5t \u0111i\u1ec3m $v(t)=s^\\prime(t)$<\/span>.<\/p>","answer":"Ch\u1ecdn A.<\/strong> t = 1s<\/span><\/p>Ta tính \u0111\u01b0\u1ee3c $s^\\prime(t)=3t^2-6t+9$<\/span>.<\/p>V\u1eadn t\u1ed1c c\u1ee7a ch\u1ea5t \u0111i\u1ec3m $v(t)=s^\\prime(t)=3t^2-6t+9=3(t-1)^2+6 \\ge 6$<\/span>.<\/p>D\u1ea5u "=" x\u1ea3y ra ⇔ t = 1.<\/p>","type":"choose","extra_type":"shape1","user_id":"131","test":"0","date":"2024-08-04 01:33:33","option_type":"txt","len":0}]}