Question

The greatest value of function $f(x)=2|x{|}^3+3x^2-12|x|+1$, 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 $g(t)=2t^3+3t^2-12t+1$
$\therefore g^{\prime }(t)=6(t+2)(t-1)$

$\therefore g(0)=1$
$g(1)=-6$
and $g(2)=5$, is the greatest value of function.