Question

Cho hàm số \(f\left(x\right)=\dfrac{x^2+x+\sqrt{x}}{x+1}\). Tìm tập nghiệm bpt \(f'\left(x\right)-1>0\)?

Answer 1

\(f\left(x\right)=x+\dfrac{\sqrt{x}}{x+1}\Rightarrow f'\left(x\right)=1+\dfrac{1-x}{2\sqrt{x}\left(x+1\right)^2}\)

\(f'\left(x\right)-1>0\Leftrightarrow\dfrac{1-x}{2\sqrt{x}\left(x+1\right)^2}>0\)

\(\Rightarrow0< x< 1\)