Question:
Prove that the function f given by $f(x)=x^{3}-3 x^{2}+4 x$ is strictly increasing on $R$ ?
Solution:
given $f(x)=x^{3}-3 x^{2}+4 x$
$\therefore f(x)=3 x^{2}-6 x+4$
$=3\left(x^{2}-2 x+1\right)+1$
$=3(x-1)^{2}+1>0$ for all $x \in R$
Hence $f(x)$ is strickly increasing on $R$