Giải bài tập 1.6 trang 9 SGK Toán 12 tập 1 - Cùng khám phá

Cho hàm số \(y = f(x)\)có đạo hàm là \(y' = f'(x) = x{(x - 1)^2}(x + 3)\)với \(\forall x \in R\) , xác định các khoảng đồng biến nghịch biến và điểm cực trị của hàm sô \(f(x)\) đã cho

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Đề bài

Phương pháp giải - Xem chi tiết

Bước 1: Xét \(f'(x) = 0\) Bước 2: Lập bảng biến thiên Bước 3: Xác định khoảng đồng biến, nghịch biến và cực trị của hàm số dựa vào bảng biến thiên

Lời giải chi tiết

Xét \(y' = f'(x) = 0\) \( \Rightarrow x{(x - 1)^2}(x + 3) = 0\) \( \Rightarrow \left[ \begin{array}{l}x = 0\\x = 1\\x = - 3\end{array} \right.\) Từ đó ta có bảng biến thiên là

Từ bảng biến thiên ta có Hàm số \(y = f(x)\) đồng biến trên khoảng\(( - \infty ; - 3),(0, + \infty )\) Hàm số \(y = f(x)\) nghịch biến trên khoảng\(( - 3;0)\) Hàm số \(y = f(x)\) đạt giá trị cực đại \(x = - 3\) Hàm số \(y = f(x)\) đạt giá trị cực tiểu tại \(x = 0\)

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🦂 Giải bài tập 1.7 trang 9 SGK Toán 12 tập 1 - Cùng khám phá Thể tích \(V\) của 1 kg nước (tính bằng cm3¬) ở nhiệt độ \(T\) (đơn vị: oC) khi \(T\) thay đổi từ 0oC đến 30oC được cho xấp xỉ bởi công thức: \(V = 999,87 - 0.06426T + 0,0085043{T^2} - 0,0000769{T^3}\) (Nguồn: James Stewart,J(2015).Calculus.Cengage Learning 8th edition, p.284) Tìm nhiệt độ \({T_0} \in (0;30)\) kể từ nhiệt độ \({T_0}\) trở lên thì thể tích tăng( làm tròn kết quả đến hàng đơn vị
꧟ Giải bài tập 1.8 trang 9 SGK Toán 12 tập 1 - Cùng khám phá Một công ty tiến hành khai thác 17 giếng dầu trong khi vực đucợ định, Trung bình mỗi giếng dầu chiết xuất đc 245 thùng dầu mỗi ngày. Công ty có thể khai thác nhiều hơn 17 giếng dầu nhưng cứ khai thác thêm một giếng thì lượng dầu mỗi giếng chiết xuất được hằng ngày giảm 9 thùng. Để giám đóc công ty có thể quyết định số giếng cần thêm cho phù hợp với tài chính, hãy chỉ ra số giếng công ty có thể khai thác thêm để sản lượng dầu chiết xuất tăng lên
💎 Giải bài tập 1.4 trang 9 SGK Toán 12 tập 1 - Cùng khám phá a) (y = - {x^3} + 3x - 6) b) (y = frac{{x - 1}}{{x + 2}}) c) (y = frac{{ - {x^2} + 2x + 2}}{{x + 1}}) d) (y = frac{{3x}}{{{x^2} - 9}})
♛ Giải bài tập 1.5 trang 9 SGK Toán 12 tập 1 - Cùng khám phá Cho hàm số \(y = f(x)\)liên tục trên đoạn \([0;3]\) thõa mãn \(f'\left( {\frac{1}{3}} \right) = f'(1) = f'\left( {\frac{5}{2}} \right) = 0\)và có đồ thị là đường cong như hình 1.5. Xác định các khoảng đơn điệu và tìm cực trị hàm số đã cho trên khoảng \((0;3)\)
꧙ Giải bài tập 1.3 trang 9 SGK Toán 12 tập 1 - Cùng khám phá a) (y = frac{x}{3}{(x - 3)^2}) b) (y = left| x right|) c) (y = {3^{x - 2{x^2}}}) d) (y = ln ({x^2} + e))

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