Chủ đề này có 1 trả lời

[hapuvotan]

 tìm min: $\sqrt{-x^{2} +4x+21 } - \sqrt{-x^{2}+3x+10}$

[Kaito Kuroba]

 tìm min: $\sqrt{-x^{2} +4x+21 } - \sqrt{-x^{2}+3x+10}$

ĐK: $$2\leq x\leq 5$$

xét: $$f_{(x)}=\sqrt{-x^{2} +4x+21 } - \sqrt{-x^{2}+3x+10}$$

$\rightarrow f'_{(x)}=\frac{-x+2}{\sqrt{-x^2+4x+21}}+\frac{2x-3}{2\sqrt{-x^2+3x+10}}$

$f'_{(x)}=0\Leftrightarrow x=\frac{1}{3}$

$\Rightarrow Min f_{(x)}=f_{(\frac{1}{3})}=\sqrt{2}$