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

increasing in the neighbourhood of x = a

Since g(x) is continuous at x = a and g(a) > 0

∴  g(x) > 0 for all x belonging in the neighbourhood of $x=\pi$

⇒ f'(x) > 0 for all x in the neighbourhood of x = a           [∵ $x^2-a x+a^2>0$ for all $x \in R$]

⇒ f(x) is increasing in the neighbourhood of x = a