what does " the absolute maximum value" mean? The absolute maximum value of $f\left(x\right) = x^3-3x^2+12$ on closed interval $\left[-2,4\right]$ occurs at $x = $ 
Confused what does absolute maximum value means. 
Does it mean 


*

*The largest of the large values? $\max \{f\left(x\right)\mid x\in [-2,4]\}$

*The largest absolute value of $\max \{\vert f\left(x\right)\vert : x\in [-2,4]\}$


I have figured out that both values are the same when $x=4$, I can see that just from the graph of the  function 


I would guess it is your first option. A usual terminology in calculus is about absolute and relative (or local) maxima and minima. 
The absolute maximum would be then $\max\{f(x):\ x\in[-2,4]\}$. 
The phrase "absolute maximum value" probably has to do with the fact that when looking at extrema of functions, one usually focus on where they are (i.e. $x=\ldots$) rather than what they are (i.e. $f(x)=\ldots$). The latter is the value, so saying "absolute maximum value" one wants the answer "$28$" as opposed "$x=4$". 
