Question

Test whether the following function is increasing or decreasing
$f\left(x\right)=x^3-6x^2+12x-16,x\in R$

Answer 1

$f\left(x\right)=x^3-6x^2+12x-16$

$f^{\prime }\left(x\right)=3x^2-12x+12$

Put x = 1

$f^{\prime }\left(1\right)=3(1{)}^2-12(1)+12$

$f^{\prime }\left(1\right)=3-12+12$

$f^{\prime }\left(1\right)=3>0\Rightarrow f^{\prime }\left(x\right)>0,$ so, f(x) is an increasing function