Consider the function $\displaystyle {f{{\left({x}\right)}}}=-{2}{x}^{{3}}+{27}{x}^{{2}}-{48}{x}+{6}$. For this function there are three important open intervals: $\displaystyle {\left(-\infty,{A}\right)}$, $\displaystyle {\left({A},{B}\right)}$, and $\displaystyle {\left({B},\infty\right)}$ where $\displaystyle {A}$ and $\displaystyle {B}$ are the critical numbers.
Find $\displaystyle {A}$ Preview Question 6 Part 1 of 7  
and $\displaystyle {B}$ Preview Question 6 Part 2 of 7  

For each of the following open intervals, determine whether $\displaystyle {f{{\left({x}\right)}}}$ is increasing or decreasing.
$\displaystyle {\left(-\infty,{A}\right)}$: Select an answer increasing decreasing
$\displaystyle {\left({A},{B}\right)}$: Select an answer increasing decreasing
$\displaystyle {\left({B},\infty\right)}$: Select an answer increasing decreasing

Using the First Derivative Test, we can conclude:

at $\displaystyle {x}={A},{f{{\left({x}\right)}}}$ has a Select an answer local maximum local minimum neither a max nor a min
at $\displaystyle {x}={B},{f{{\left({x}\right)}}}$ has a Select an answer local maximum local minimum neither a max nor a min