Question

The greatest value of function $f(x)=2|x|^3+3 x^2-12|x|+1$, where $x \in[-1,2]$ is equal to

• A. 5
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (A)

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.