Question

The intervals of increase of $f(x)$ defined by $f(x)=\int\limits_{-1}^{x}\left(t^{2}+2 t\right)\left(t^{2}-1\right) d t$ is equal to

• A. $\left(-\infty, \frac{-3}{2}\right) \cup(0,3) \cup(10, \infty)$
• B. $(-\infty,-2) \cup(-1,0) \cup(1, \infty)$
• C. $(-\infty,-2) \cup\left(\frac{-1}{2}, \frac{1}{2}\right) \cup(4, \infty)$
• D. $(-\infty,-2) \cup\left(\frac{-3}{4}, \frac{1}{4}\right) \cup(1, \infty)$

Answer 1

Answer: (B)

We have $\mathrm{f}^{\prime}(\mathrm{x})=\mathrm{x}(\mathrm{x}+2)(\mathrm{x}+1)(\mathrm{x}-1)$