If $g \left(x\right)$ is a continuous function at $x = a$ such that $g\left(a\right) > 0$ and $f\text{'}\left(x\right)=g\left(x\right)(x^2-ax+a^2)$ for all $x\in R,$ then $f\left(x\right),$ is 

Since $g \left(x\right)$ is continuous at $x = a$ and $g \left(a\right) > 0.$

$\therefore g\left(x\right)>0$ for all $x$ belonging in the neighbourhood of $x = a$

$\Rightarrow f\text{'}\left(x\right)>0$ for all $x$ in the neighbourhood of $x = a$

                                                 $\left[\because x^2-ax+a^2>0\right.$ for all $x\in R]$

$\Rightarrow f\left(x\right)$ is increasing in the neighbourhood of $x = a$