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 


It means your first assumption. 
Setting the derivative equal to $0$, we obtain:
$3x^2 - 6x = 0  \Rightarrow$
$x(3x - 6)=0 \Rightarrow$ 
$x=0,$ or $x=2$
$f(2) = 8$, $f(0) = 12$
Now we test end points,
$f(4) = 64 - 48 + 12 = 28$ 
$f(-2)= -8 -12 + 12 = -8$
Hence $f(4)=28$ = $\max \{ f(x): x \in [-2,4]\}$ 
