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
Answer & explanation
Correct answer: option 1
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