Tìm tất cả các giá trị của m để y = x + 16/x + m đồng biến trên (0;16) 03/10/2021 Bởi Reagan Tìm tất cả các giá trị của m để y = x + 16/x + m đồng biến trên (0;16)
$$\eqalign{ & y = x + {{16} \over x} + m\,\,DB/\left( {0;16} \right) \cr & y’ = 1 – {{16} \over {{x^2}}} = 0 \Leftrightarrow {{{x^2} – 16} \over {{x^2}}} = 0 \Leftrightarrow x = \pm 4 \cr & BXD: \cr & x\,\,\,\,\,\,\, – \infty \,\,\,\,\,\,\,\,\,\,\,\, – 4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4\,\,\,\,\,\,\,\,\,\,\,\, + \infty \cr & y’\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, + \,\,\,\,\,\,\,\,0\,\,\,\,\,\,\, – \,\,\,\,\,\,\,0\,\,\,\,\,\,\,\, + \cr & \Rightarrow Hs\,\,DB/\left( { – \infty ; – 4} \right);\,\,\left( {4; + \infty } \right) \cr & \Rightarrow Khong\,\,ton\,\,tai\,\,m\,\,de\,ham\,\,so\,\,DB/\left( {0;16} \right) \cr} $$ Bình luận
$$\eqalign{
& y = x + {{16} \over x} + m\,\,DB/\left( {0;16} \right) \cr
& y’ = 1 – {{16} \over {{x^2}}} = 0 \Leftrightarrow {{{x^2} – 16} \over {{x^2}}} = 0 \Leftrightarrow x = \pm 4 \cr
& BXD: \cr
& x\,\,\,\,\,\,\, – \infty \,\,\,\,\,\,\,\,\,\,\,\, – 4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4\,\,\,\,\,\,\,\,\,\,\,\, + \infty \cr
& y’\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, + \,\,\,\,\,\,\,\,0\,\,\,\,\,\,\, – \,\,\,\,\,\,\,0\,\,\,\,\,\,\,\, + \cr
& \Rightarrow Hs\,\,DB/\left( { – \infty ; – 4} \right);\,\,\left( {4; + \infty } \right) \cr
& \Rightarrow Khong\,\,ton\,\,tai\,\,m\,\,de\,ham\,\,so\,\,DB/\left( {0;16} \right) \cr} $$