Chú ý: Để đảm bảo quyền lợi và bảo vệ tài khoản của mình
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{"common":{"save":0,"post_id":"7128","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5974","post_id":"7128","mon_id":"1158924","chapter_id":"1159187","question":"<p>Cho hàm s\u1ed1 <span class=\"math-tex\">$f(x)=e^{x-x^2}$<\/span>. Bi\u1ebft ph\u01b0\u01a1ng trình <span class=\"math-tex\">$f^{\\prime\\prime}(x)=0$<\/span> có hai nghi\u1ec7m <span class=\"math-tex\">$x_1,x_2$<\/span>. Tính tích <span class=\"math-tex\">$x_1.x_2$<\/span>.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$-\\dfrac{1}{4}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$1$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{3}{4}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$0$<\/span>"],"correct":"1","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> <span class=\"math-tex\">$-\\dfrac{1}{4}$<\/span>.<\/span><\/p><p><span class=\"math-tex\">$f(x)=e^{x-x^2}$<\/span><\/p><p><span class=\"math-tex\">$f^\\prime(x)=(1-2x)e^{x-x^2}$<\/span><\/p><p><span class=\"math-tex\">$f^{\\prime\\prime}(x)=-2e^{x-x^2}+(1-2x)^2e^{x-x^2}$<\/span> <span class=\"math-tex\">$=(4x^2-4x-1)e^{x-x^2}$<\/span><\/p><p><span class=\"math-tex\">$f^{\\prime\\prime}(x)=0$<\/span> ⇔ <span class=\"math-tex\">$(4x^2-4x-1)e^{x-x^2}=0$<\/span> ⇔ <span class=\"math-tex\">$4x^2-4x-1=0$<\/span> (vì <span class=\"math-tex\">$e^{x-x^2}\\ne0;\\forall x\\in R$<\/span>).<\/p><p>Khi \u0111ó <span class=\"math-tex\">$x_1.x_2=\\dfrac{c}{a}=-\\dfrac{1}{4}$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-05-30 04:14:05","option_type":"math","len":0},{"id":"5977","post_id":"7128","mon_id":"1158924","chapter_id":"1159187","question":"<p>Cho chuy\u1ec3n \u0111\u1ed9ng th\u1eb3ng xác \u0111\u1ecbnh b\u1edfi ph\u01b0\u01a1ng trình <span class=\"math-tex\">$s(t)=2t^3-5t^2+3t$<\/span>, trong \u0111ó t \u0111\u01b0\u1ee3c tính b\u1eb1ng giây và s \u0111\u01b0\u1ee3c tính b\u1eb1ng mét. V\u1eadn t\u1ed1c t\u1ee9c th\u1eddi c\u1ee7a v\u1eadt t\u1ea1i th\u1eddi \u0111i\u1ec3m gia t\u1ed1c b\u1eb1ng 14 m\/s² là<\/p>","options":["<strong>A.<\/strong> 14 m\/s","<strong>B.<\/strong> –7 m\/s","<strong>C.<\/strong> 7 m\/s","<strong>D.<\/strong> –14 m\/s"],"correct":"3","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> 7 m\/s.<\/span><\/p><p><span class=\"math-tex\">$s(t)=2t^3-5t^2+3t$<\/span><\/p><p><span class=\"math-tex\">$v(t)=s^\\prime(t)=6t^2-10t+3$<\/span><\/p><p><span class=\"math-tex\">$a(t)=v^\\prime(t)=12t-10$<\/span><\/p><p>Gia t\u1ed1c b\u1eb1ng 14 m\/s² khi <span class=\"math-tex\">$12t-10=14$<\/span> ⇔ <span class=\"math-tex\">$t=2$<\/span> giây.<\/p><p>V\u1eadn t\u1ed1c c\u1ea7n tìm là <span class=\"math-tex\">$v(2)=7$<\/span> m\/s.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-05-30 04:25:43","option_type":"txt","len":2},{"id":"5978","post_id":"7128","mon_id":"1158924","chapter_id":"1159187","question":"<p>M\u1ed9t ch\u1ea5t \u0111i\u1ec3m chuy\u1ec3n \u0111\u1ed9ng theo ph\u01b0\u01a1ng trình <span class=\"math-tex\">$s(t)=3\\sin2t+\\cos2t$<\/span> v\u1edbi t (giây) là kho\u1ea3ng th\u1eddi gian tính t\u1eeb khi v\u1eadt b\u1eaft \u0111\u1ea7u chuy\u1ec3n \u0111\u1ed9ng và s (mét) là quãng \u0111\u01b0\u1eddng v\u1eadt \u0111i \u0111\u01b0\u1ee3c trong th\u1eddi gian \u0111ó. Gia t\u1ed1c t\u1ee9c th\u1eddi t\u1ea1i th\u1eddi \u0111i\u1ec3m<br \/>t = <span class=\"math-tex\">$\\dfrac{\\pi}{4}$<\/span> giây c\u1ee7a chuy\u1ec3n \u0111\u1ed9ng b\u1eb1ng<\/p>","options":["<strong>A.<\/strong> –16 m\/s²","<strong>B.<\/strong> –12 m\/s²","<strong>C.<\/strong> 0 m\/s²","<strong>D.<\/strong> 16 m\/s²"],"correct":"2","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> –12 m\/s².<\/span><\/p><p><span class=\"math-tex\">$s(t)=3\\sin2t+\\cos2t$<\/span><\/p><p><span class=\"math-tex\">$v(t)=\u200b\u200bs^\\prime(t)=6\\cos2t-2\\sin2t$<\/span><\/p><p><span class=\"math-tex\">$a(t)=v^\\prime(t)=-12\\sin2t-4\\cos2t$<\/span><\/p><p>Gia t\u1ed1c t\u1ee9c th\u1eddi t\u1ea1i th\u1eddi \u0111i\u1ec3m t = <span class=\"math-tex\">$\\dfrac{\\pi}{4}$<\/span> là <span class=\"math-tex\">$a\\bigg(\\dfrac{\\pi}{4}\\bigg)=-12\\sin\\dfrac{\\pi}{2}-4\\cos\\dfrac{\\pi}{2}=-12$<\/span> m\/s².<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-05-30 04:32:48","option_type":"txt","len":2}]}