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PT
1
PT
1
PT
1
CM
6 tháng 10 2019
Đáp án B
Hàm số y = x + 1 3 (5 - x) xác định trên R.
y' = - x + 1 3 + 3 x + 1 2 (5 - x) = 2 x + 1 2 (7 - 2x)
y' = 0 ⇔ 
Bảng biến thiên
Suy ra hàm số chỉ có một cực trị (là cực đại)
Cách khác: Nhận xét rằng y' chỉ đổi dấu khi x đi qua 7/2 nên hàm số chỉ có một cực trị
PT
1
CM
7 tháng 10 2019
Đáp án: D.
Hàm số y = x 4 - 5 x 2 + 4 xác định trên R.
y' = 4 x 3 - 10x = 2x(2 x 5 - 5);
y' = 0 khi
y'' = 12 x 2 - 10
Vì y''(0) = -10 < 0,
nên hàm số chỉ có một cực đại (tại x = 0)
Cách khác: Vì a > 0 và y' = 0 có ba nghiệm phân biệt nên hàm số y = a x 4 + b x 2 + c có một cực đại
PT
1
CM
30 tháng 9 2019
Đáp án: D.
Hàm số y = x 4 - 5 x 2 + 4 xác định trên R.
y' = 4 x 3 - 10x = 2x(2 x 2 - 5);
y' = 0 khi
y'' = 12 x 2 - 10
Vì y''(0) = -10 < 0,
nên hàm số chỉ có một cực đại (tại x = 0)
Cách khác: Vì a > 0 và y' = 0 có ba nghiệm phân biệt nên hàm số y = a x 4 + b x 2 + c có một cực đại
PT
1
CM
9 tháng 9 2019
Đáp án: B.
Hàm số y = ( x + 1 ) 3 (5 - x) xác định trên R.
y' = - ( x + 1 ) 3 + 3 ( x + 1 ) 2 (5 - x) = 2 ( x + 1 ) 2 (7 - 2x)
y' = 0 ⇔ 
Bảng biến thiên
Suy ra hàm số chỉ có một cực trị (là cực đại)
Cách khác: Nhận xét rằng y' chỉ đổi dấu khi x đi qua 7/2 nên hàm số chỉ có một cực trị
LT
0
ND
Nguyễn Đức Trí
VIP
9 tháng 8 2023
\(y=x^8+\left(m-2\right)x^5-4\left(m^2-4\right)+1\)
Tập xác định \(D=ℝ\)
\(y'=8x^7+5\left(m-2\right)x^4\)
\(y''=56x^6+20\left(m-2\right)x^3\)
Để hàm số đạt cực tiểu tại \(x=0\)
\(\left\{{}\begin{matrix}y'\left(0\right)=0\\y''\left(0\right)>0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}0m=0\\0m>0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\forall m\inℝ\\m>0\end{matrix}\right.\) \(\Leftrightarrow m>0\)
Vậy \(m>0\) hàm số trên đạt cực tiểu tại \(x=0\)
TD
9 tháng 8 2023
Với đề thi THPT quốc gia môn Toán, đây là một trong những câu khó. Không nhiều các bạn học sinh giải được đề toán trên. Đây là một hàm số bậc 8, hoàn toàn khác với những hàm số thông dụng được học trên lớp, để giải được bài này, các bạn cần phải sử dụng kiến thức từ định nghĩa và tính chất của cực trị hàm số bất kì. Ta có:
y" = 8x7 + 5(m - 2)x4 - 4(m2 - 4)x3 + 1
Hàm đạt cực tiểu tại x = 0 thì y"(x) = 0 và y"(x) đổi dấu từ âm sang dương khi x chạy qua điểm 0. Từ đó ta tương đương với số hạng chứa x có lũy thừa thấp nhất có hệ số khác 0 trong biểu thức y’ là lũy thừa bậc lẻ, hệ số dương.
Có nghĩa là :
–4(m2 - 4) > 0 và m - 2 = m² – 4 = 0
⇔ –2 Bài 2 - Mã đề 124 đề thi môn Toán THPT Quốc gia 2017
Dưới đây là hàm số y = f(x) được thể hiện trong bình với bảng biến thiên:
Tìm giá trị cực tiểu, cực đại của hàm số đã cho.
Bài giải:
Theo như bảng biến thiên các em học sinh nhận thấy được cực tiểu là 0 và giá trị cực đại của hàm số là 3.
Nhiều câu hỏi cho sẵn bảng biến thiên hay hình vẽ đồ thị hàm số sẽ xuất hiện trong đề thi. Chúng ta có thể vận dụng chính những dữ liệu này để có cho mình được đáp án đúng một cách nhanh chóng.
Đây nhé bro:))!
CM
19 tháng 1 2017
Đồ thị hàm số y = | x | 3 - 2 x 2 + | x | + 1 có dạng như hình (2)
Số nghiệm của phương trình | x | 3 - 2 x 2 + | x | + 1 = m là số giao điểm của đồ thị hàm số y = | x | 3 - 2 x 2 + | x | + 1 và đường thẳng y = m.
Số nghiệm của phương trình y = | x | 3 - 2 x 2 + | x | + 1 là số giao điểm của đồ thị hàm số và đường thẳng y = m.
Dựa vào đồ thị với m > 0 phương trình có tối thiểu 0 nghiệm ( 0 nghiệm – tức là phương trình vô nghiệm).
Chọn A
CM
17 tháng 9 2017
s i n 2 x + c o s x = m <=> - c o s x 2 x + c o s x + 1 = 0
Đặt t= cos x =>
=>f’(t)=-2t + 1.
Do x ∈ [0; π] => t ∈ [-1; 1]
Số nghiệm của phương trình đã cho chính là số giao điểm của đồ thị hàm số y = f(t) và đường thẳng y = m.
Từ bảng biến thiên ta có m ∈ (-1; 1) thì f(t)=m có 2 nghiệm
Chọn C
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nhiều quá
:)) , 0 là tiền đề của cộng,trừ vô cùng , bạn cần giải mấy bài lim à ?