Mathematics - Application of Derivative Question with Solution | TestHub

The ordinates of any point on the curve is given by $y=\frac{x^3}{(x-a{)}^2}\cdot \frac{dy}{dx}=\frac{x^2(x-3a)}{(x-a{)}^3}$. Now, $\frac{dy}{dx}=0\Rightarrow x=0$ or $x=3a$. ${\frac{d^{2}y}{d{x}^2}|}_{x=0}=0$ and ${\frac{d^{2}y}{d{x}^2}|}_{x=3a}=\frac{72a^5}{(2a{)}^6}>0$. Hence $y$ is minimum at $x=3a$ and is equal to $\frac{27a}{4}$.