`y=x^3+5x^2-15x+1`
TXĐ: `D=RR`
`y'=3x^2+10x-15`
`y'=0<=>3x^2+10x-15=0`
`<=>`\(\left[ \begin{array}{l}x=\dfrac{-5+\sqrt{70}}{3}\\x=\dfrac{-5-\sqrt{70}}{3}\end{array} \right.\)
BBT:
\begin{array}{|c|cc|}\hline \text{$x$}&\text{$-\infty$}&\text{}&\text{$\dfrac{-5-\sqrt{70}}{3}$}&\text{}&\text{$\dfrac{-5+\sqrt{70}}{3}$}&\text{}&\text{$+\infty$}\\\hline \text{$y'$}&\text{}&+\text{}&\text{0}&-\text{}&\text{0}&+\text{}&\text{}\\\hline \text{$y$}&\text{}&\text{}\nearrow&\text{}&\text{}\searrow&\text{}&\text{}\nearrow\\\hline \end{array}
Vậy hàm số đồng biến trên khoảng : `(-\infty;(-5-\sqrt{70})/(3))` và `((-5+\sqrt{70})/(3);+\infty)`
Hàm số nghịch biến trên khoảng `((-5-\sqrt{70})/(3);(-5+\sqrt{70})/(3))`
