{"common":{"save":0,"post_id":"7127","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5952","post_id":"7127","mon_id":"1158924","chapter_id":"1159187","question":"<p>Tính \u0111\u1ea1o hàm c\u1ea5p hai c\u1ee7a hàm s\u1ed1 <span class=\"math-tex\">$f(x)=\\dfrac{1}{2x-1}$<\/span> t\u1ea1i x = –1.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$-\\dfrac{8}{27}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\dfrac{2}{9}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$-\\dfrac{2}{9}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\dfrac{8}{27}$<\/span>"],"correct":"1","level":"2","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> <span class=\"math-tex\">$-\\dfrac{8}{27}$<\/span>.<\/span><\/p><p>T\u1eadp xác \u0111\u1ecbnh D = R\\<span class=\"math-tex\">$\\bigg\\{\\dfrac{1}{2}\\bigg\\}$<\/span>.<\/p><p><span class=\"math-tex\">$f(x)=\\dfrac{1}{2x-1}$<\/span> ⇒ <span class=\"math-tex\">$f^\\prime(x)=\u200b\u200b\\dfrac{-2}{(2x-1)^2}$<\/span> ⇒ <span class=\"math-tex\">$f^{\\prime\\prime}(x)=\\dfrac{2.2.2(2x-1)}{(2x-1)^4}=\\dfrac{8}{(2x-1)^3}$<\/span><\/p><p>Do \u0111ó <span class=\"math-tex\">$f^{\\prime\\prime}(-1)=\\dfrac{8}{(-2-1)^3}=-\\dfrac{8}{27}$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-05-30 02:31:50","option_type":"math","len":0},{"id":"5954","post_id":"7127","mon_id":"1158924","chapter_id":"1159187","question":"<p>Tính \u0111\u1ea1o hàm c\u1ea5p hai c\u1ee7a hàm s\u1ed1 <span class=\"math-tex\">$f(x)=x^3+2x$<\/span> t\u1ea1i x = 1.<\/p>","options":["<strong>A.<\/strong> 3","<strong>B.<\/strong> 6","<strong>C.<\/strong> 8","<strong>D.<\/strong> 2"],"correct":"2","level":"2","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> 6.<\/span><\/p><p><span class=\"math-tex\">$f(x)=x^3+2x$<\/span> ⇒ <span class=\"math-tex\">$f^\\prime(x)=3x^2+2$<\/span> ⇒ <span class=\"math-tex\">$f^{\\prime\\prime}(x)=6x$<\/span>.<\/p><p>Do \u0111ó <span class=\"math-tex\">$f^{\\prime\\prime}(1)=6.1=6$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-05-30 02:35:01","option_type":"txt","len":0},{"id":"5956","post_id":"7127","mon_id":"1158924","chapter_id":"1159187","question":"<p>Tính \u0111\u1ea1o hàm c\u1ea5p hai c\u1ee7a hàm s\u1ed1 <span class=\"math-tex\">$y=\\sin^2x$<\/span> t\u1ea1i x = <span class=\"math-tex\">$\\pi$<\/span>.<\/p>","options":["<strong>A.<\/strong> –2","<strong>B.<\/strong> 1","<strong>C.<\/strong> 2","<strong>D.<\/strong> –1"],"correct":"3","level":"2","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> 2.<\/span><\/p><p><span class=\"math-tex\">$y=\\sin^2x$<\/span> ⇒ <span class=\"math-tex\">$y^\\prime=2\\cos x.\\sin x=\\sin2x$<\/span> ⇒ <span class=\"math-tex\">$y^{\\prime\\prime}=2\\cos2x$<\/span><\/p><p>Do \u0111ó <span class=\"math-tex\">$y^{\\prime\\prime}(\\pi)=2.\\cos2\\pi=2$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-05-30 02:41:15","option_type":"txt","len":1}]}
