{"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 h&agrave;m s\u1ed1&nbsp;<span class=\"math-tex\">$f(x)=e^{x-x^2}$<\/span>. Bi\u1ebft ph\u01b0\u01a1ng tr&igrave;nh&nbsp;<span class=\"math-tex\">$f^{\\prime\\prime}(x)=0$<\/span>&nbsp;c&oacute; hai nghi\u1ec7m&nbsp;<span class=\"math-tex\">$x_1,x_2$<\/span>. T&iacute;nh t&iacute;ch&nbsp;<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&nbsp;<span style=\"color:#16a085;\"><strong>A.<\/strong>&nbsp;<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>&nbsp;<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>&nbsp;&hArr;&nbsp;<span class=\"math-tex\">$(4x^2-4x-1)e^{x-x^2}=0$<\/span>&nbsp;&hArr;&nbsp;<span class=\"math-tex\">$4x^2-4x-1=0$<\/span>&nbsp;(v&igrave;&nbsp;<span class=\"math-tex\">$e^{x-x^2}\\ne0;\\forall x\\in R$<\/span>).<\/p><p>Khi \u0111&oacute;&nbsp;<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 x&aacute;c \u0111\u1ecbnh b\u1edfi ph\u01b0\u01a1ng tr&igrave;nh <span class=\"math-tex\">$s(t)=2t^3-5t^2+3t$<\/span>, trong \u0111&oacute; t&nbsp;\u0111\u01b0\u1ee3c t&iacute;nh&nbsp;b\u1eb1ng gi&acirc;y v&agrave; s \u0111\u01b0\u1ee3c t&iacute;nh b\u1eb1ng m&eacute;t. 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\/s&sup2;&nbsp;l&agrave;<\/p>","options":["<strong>A.<\/strong> 14 m\/s","<strong>B.<\/strong> &ndash;7 m\/s","<strong>C.<\/strong> 7 m\/s","<strong>D.<\/strong> &ndash;14 m\/s"],"correct":"3","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<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\/s&sup2; khi&nbsp;<span class=\"math-tex\">$12t-10=14$<\/span>&nbsp;&hArr;&nbsp;<span class=\"math-tex\">$t=2$<\/span>&nbsp;gi&acirc;y.<\/p><p>V\u1eadn t\u1ed1c c\u1ea7n t&igrave;m l&agrave;&nbsp;<span class=\"math-tex\">$v(2)=7$<\/span>&nbsp;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 tr&igrave;nh&nbsp;<span class=\"math-tex\">$s(t)=3\\sin2t+\\cos2t$<\/span>&nbsp;v\u1edbi t&nbsp;(gi&acirc;y) l&agrave; kho\u1ea3ng th\u1eddi&nbsp;gian t&iacute;nh t\u1eeb khi v\u1eadt b\u1eaft \u0111\u1ea7u chuy\u1ec3n \u0111\u1ed9ng v&agrave; s&nbsp;(m&eacute;t) l&agrave; qu&atilde;ng \u0111\u01b0\u1eddng v\u1eadt \u0111i \u0111\u01b0\u1ee3c trong th\u1eddi gian&nbsp;\u0111&oacute;. Gia t\u1ed1c t\u1ee9c th\u1eddi t\u1ea1i th\u1eddi \u0111i\u1ec3m<br \/>t =&nbsp;<span class=\"math-tex\">$\\dfrac{\\pi}{4}$<\/span> gi&acirc;y c\u1ee7a chuy\u1ec3n \u0111\u1ed9ng b\u1eb1ng<\/p>","options":["<strong>A.<\/strong> &ndash;16 m\/s&sup2;","<strong>B.<\/strong> &ndash;12 m\/s&sup2;","<strong>C.<\/strong> 0 m\/s&sup2;","<strong>D.<\/strong> 16 m\/s&sup2;"],"correct":"2","level":"3","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>B.<\/strong>&nbsp;&ndash;12 m\/s&sup2;.<\/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 =&nbsp;<span class=\"math-tex\">$\\dfrac{\\pi}{4}$<\/span>&nbsp;l&agrave;&nbsp;<span class=\"math-tex\">$a\\bigg(\\dfrac{\\pi}{4}\\bigg)=-12\\sin\\dfrac{\\pi}{2}-4\\cos\\dfrac{\\pi}{2}=-12$<\/span>&nbsp;m\/s&sup2;.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-05-30 04:32:48","option_type":"txt","len":2}]}