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Q.
The greatest value of function $f(x)=2|x|^3+3 x^2-12|x|+1$, where $x \in[-1,2]$ is equal to
Application of Derivatives
Solution:
Put $|x|=t$
As, $x \in[-1,2] \Rightarrow t \in[0,2]$
let $g(t)=2 t^3+3 t^2-12 t+1$
$\therefore g ^{\prime}( t )=6( t +2)( t -1)$
$\therefore g (0) =1 $
$g (1) =-6$
and $g (2)=5$, is the greatest value of function.
