Question

Show that the function $f\left(x\right)=x^3-3x^2+6x-100$ is increasing on R.

Answer 1

$\frac{d}{dx}\left(f\right(x\left)\right)=3x^2-6x+6$

Discriminant of $\frac{d}{dx}\left(f\right(x\left)\right)$ $=36-4\left(6\right)\left(3\right)=-36<0$

The coefficient of $x^2=3>0$