{"common":{"save":0,"post_id":"7125","level":1,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5932","post_id":"7125","mon_id":"1158924","chapter_id":"1159187","question":"<p>Cho hàm s\u1ed1 <span class=\"math-tex\">$y=x^5-3x^4+x+1$<\/span> v\u1edbi x ∈ R. \u0110\u1ea1o hàm <span class=\"math-tex\">$y^{\\prime\\prime}$<\/span> c\u1ee7a hàm s\u1ed1 là<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$5x^3-12x^2+1$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$5x^4-12x^3$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$20x^2-36x^3$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$20x^3-36x^2$<\/span>"],"correct":"4","level":"1","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D.<\/strong> <span class=\"math-tex\">$20x^3-36x^2$<\/span>.<\/span><\/p><p><span class=\"math-tex\">$y=x^5-3x^4+x+1$<\/span><\/p><p>⇒ <span class=\"math-tex\">$y^\\prime=5x^4-12x^3+1$<\/span><\/p><p>⇒ <span class=\"math-tex\">$y^{\\prime\\prime}=20x^3-36x^2$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-05-30 01:42:42","option_type":"math","len":0},{"id":"5934","post_id":"7125","mon_id":"1158924","chapter_id":"1159187","question":"<p>\u0110\u1ea1o hàm c\u1ea5p hai c\u1ee7a hàm s\u1ed1 <span class=\"math-tex\">$y=-3\\cos x$<\/span> t\u1ea1i \u0111i\u1ec3m <span class=\"math-tex\">$x_0=\\dfrac{\\pi}{2}$<\/span>.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$-3$<\/span>","<strong>B.<\/strong> 5","<strong>C.<\/strong> 0","<strong>D.<\/strong> 3"],"correct":"3","level":"1","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> 0.<\/span><\/p><p><span class=\"math-tex\">$y=-3\\cos x$<\/span><\/p><p>⇒ <span class=\"math-tex\">$y^\\prime=3\\sin x$<\/span><\/p><p>⇒ <span class=\"math-tex\">$y^{\\prime\\prime}=3\\cos x$<\/span><\/p><p>Do \u0111ó <span class=\"math-tex\">$y^{\\prime\\prime}\\bigg(\\dfrac{\\pi}{2}\\bigg)=3\\cos \\bigg(\\dfrac{\\pi}{2}\\bigg)=0$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-05-30 01:47:00","option_type":"math","len":0},{"id":"5936","post_id":"7125","mon_id":"1158924","chapter_id":"1159187","question":"<p>Cho hàm s\u1ed1 <span class=\"math-tex\">$f(x)=(3x-7)^5$<\/span>. Tính <span class=\"math-tex\">$f^{\\prime\\prime}(2)$<\/span>.<\/p>","options":["<strong>A.<\/strong> 0","<strong>B.<\/strong> 20","<strong>C.<\/strong> –180","<strong>D.<\/strong> 30"],"correct":"3","level":"1","hint":"<p>Tìm \u0111\u1ea1o hàm b\u1eb1ng cách s\u1eed d\u1ee5ng quy t\u1eafc chu\u1ed7i, quy t\u1eafc nói r\u1eb1ng<\/p><p><span class=\"math-tex\">${d \\over dx}[f(g(x))] = f’(g(x)).g’(x)$<\/span><\/p><p>trong \u0111ó<\/p><p><span class=\"math-tex\">$f(x) = x^5, g(x) = (3x-7)$<\/span><\/p>","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> –180.<\/span><\/p><p><span class=\"math-tex\">$f(x)=(3x-7)^5$<\/span> ⇒ <span class=\"math-tex\">$f^\\prime(x)=5(3x-7)^4.(3x-7)’ = 15(3x-7)^4$<\/span> <\/p><p>⇒ <span class=\"math-tex\">$f^{\\prime\\prime}(x)=60(3x-7)^3.(3x-7)’ = 180(3x-7)^3$<\/span><\/p><p>Do \u0111ó <span class=\"math-tex\">$f^{\\prime\\prime}(2)=180(3.2-7)^3=-180$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-05-30 01:51:29","option_type":"txt","len":1}]}
