Consider the function $\displaystyle {f{{\left({x}\right)}}}={12}{x}^{{5}}+{60}{x}^{{4}}-{100}{x}^{{3}}+{2}$. For this function there are four important intervals: $\displaystyle {\left(-\infty,{A}\right]}$, $\displaystyle {\left[{A},{B}\right]}$,$\displaystyle {\left[{B},{C}\right]}$, and $\displaystyle {\left[{C},\infty\right)}$ where $\displaystyle {A}$, $\displaystyle {B}$, and $\displaystyle {C}$ are the critical numbers.
Find $\displaystyle {A}$ Preview Question 6 Part 1 of 6  
and $\displaystyle {B}$ Preview Question 6 Part 2 of 6  
and $\displaystyle {C}$ Preview Question 6 Part 3 of 6  

At each critical number $\displaystyle {A}$, $\displaystyle {B}$, and $\displaystyle {C}$ does $\displaystyle {f{{\left({x}\right)}}}$ have a local min, a local max, or neither? Type in your answer as LMIN, LMAX, or NEITHER.
At $\displaystyle {A}$
At $\displaystyle {B}$
At $\displaystyle {C}$