Question

Let $f(x)$ be a real valued continuous function satisfying $f^3(x)-5f^2(x)+10f(x)-12\le 0$ and $f^2(x)-7f(x)+12\le 0$. A ray of light coming along the curve $y=f(x)$ from positive direction of $x$-axis and strikes the inner surface of mirror $y=2\sqrt{3x}$. If $l$ is the length of the reflected ray contained within the parabola $y^2=12x$ then find the value of $12l$.

Answer 1

Answer: 225