The function f(x) =x^3-3 x^2+12 x-18 is :

Question

The function $f(x) =x^3-3 x^2+12 x-18$ is :

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Answer

$\text {} f(x)=x^3-3 x^2+12 x-18$
$\Rightarrow f^{\prime}(x)=3 x^2-6 x+12$
$=3\left(x^2-2 x+1^2\right)+9$
$=3(x-1)^2+3^2>0 \forall x \in R$
$\Rightarrow f(x) $ is strictly increasing on $ R$

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