Question

Find the intervals in which the $f\left(x\right)=x^4-8x^3+22x^2-24x+21$ is:
$\left(i\right)$ increasing
$\left(ii\right)$decreasing

Answer 1

$\begin{array}{c}f\left(x\right)=x^4-8x^3+22x^2-24x+21\\ f^{\prime }\left(x\right)=4x^3-24x^2+44x-24=0\\ \Rightarrow \left(x-1\right)\left(x-2\right)\left(x-3\right)=0\end{array}$
increasing $\left(1,2\right)\cup \left(3,\infty \right)$
decreasing $\left(-\infty ,1\right)\cup \left(2,3\right)$