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Giải bài 33 trang 71 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Cho các hàm số \(f\left( x \right) = {3^{2x - 1}}\) và \(g\left( x \right) = x{\rm{ln}}9\). Giải bất phương trình \(f'\left( x \right) < g'\left( x \right)\).

𒆙Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Cho các hàm số \(f\left( x \right) = {3^{2x - 1}}\) và \(g\left( x \right) = x{\rm{ln}}9\). Giải bất phương trình \(f'\left( x \right) < g'\left( x \right)\).

Phương pháp giải - Xem chi tiết

\({\left( {{a^u}} \right)^\prime } = u'.{a^u}.\ln a\) Tính \(f'\left( x \right);g'\left( x \right)\). Giải bất phương trình \(f'\left( x \right) < g'\left( x \right)\).

Lời giải chi tiết

Ta có \(f'\left( x \right) = 2 \cdot {3^{2x - 1}} \cdot {\rm{ln}}3;g'\left( x \right) = {\rm{ln}}9\).Khi đó: \(f'\left( x \right) < g'\left( x \right) \Leftrightarrow 2 \cdot {3^{2x - 1}} \cdot {\rm{ln}}3 < {\rm{ln}}9 \Leftrightarrow {3^{2x - 1}} < 1 \Leftrightarrow 2x - 1 < 0 \Leftrightarrow x < \frac{1}{2}\).Vậy nghiệm của bất phương trình đã cho là \(\left( { - \infty ;\frac{1}{2}} \right)\).

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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