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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
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Đề bài

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

Phương pháp giải - Xem chi tiết

Nhiệt độ \({T_0} \in (0;30)\) kể từ nhiệt độ \({T_0}\) trở lên thì thể tích tăng là tìm khoảng dông biến của hàm số \(V = 999,87 - 0.06426T + 0,0085043{T^2} - 0,0000769{T^3}\) Bước 1: Tính Bước 2: Lập bảng biến thiên Bước 3: Xác định khoảng dông biến của hàm số dựa vào bảng biến thiên

Lời giải chi tiết

Ta có: \(V' =  - 0,06426 + 2.0,0085043T - 3.0,0000769{T^2}\) Xét \(V' = 0\)\( \Rightarrow  - 0,06426 + 2.0,0085043T - 3.0,0000769{T^2} = 0\) \( \Rightarrow \left[ \begin{array}{l}T = 69\\T = 4\end{array} \right.\) Từ đó ta có bảng biến thiên là

Từ bảng biến thiên ta thấy Hàm số trên đồng biến từ \({T_0} = 4\)hay thể tích nước tăng từ khi \({T_0} = 4\)

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