Câu 11.
1.
\(f'\left(x\right)=\dfrac{3x-15+3x+1}{\left(x-5\right)^2}=\dfrac{6x-14}{\left(x-5\right)^2}\)
ĐK: \(x\ne5\)
\(f'\left(x\right)=\dfrac{6x-14}{\left(x-5\right)^2}>0\Leftrightarrow6x-14>0\Leftrightarrow x>\dfrac{7}{3}\)
Vậy \(S=(\dfrac{7}{3};+\infty]\backslash\left\{5\right\}\)
2.
\(f'\left(x\right)=\left(\dfrac{3x^2}{5x+1}\right)'+\left(\dfrac{2x}{5x+1}\right)'-\left(\dfrac{1}{5x+1}\right)'\)
\(=\dfrac{\left(3x^2\right)'.\left(5x+1\right)+3x^2.\left(5x+1\right)'}{\left(5x+1\right)^2}+\dfrac{\left(2x\right)'.\left(5x+1\right)+2x.\left(5x+1\right)'}{\left(5x+1\right)^2}\)
\(=\dfrac{45x^2+6x}{\left(5x+1\right)^2}+\dfrac{20x+2}{\left(5x+1\right)^2}=\dfrac{45x^2+26x+2}{\left(5x+1\right)^2}\)
ĐK: \(x\ne-\dfrac{1}{5}\)
\(f'\left(x\right)=\dfrac{45x^2+26x+2}{\left(5x+1\right)^2}>0\Leftrightarrow45x^2+26x+2>0\)
\(\Leftrightarrow\left[{}\begin{matrix}x< \dfrac{-13-\sqrt{79}}{45}\\x>\dfrac{-13+\sqrt{79}}{45}\end{matrix}\right.\)
\(\Leftrightarrow...\)
