Mathematics - Application of Derivative Question with Solution | TestHub

Let $\mathrm{f}(\mathrm{x})$ be a continuous function which satisfies,

${\mathrm{f}}^3(\mathrm{x})-5{\mathrm{f}}^2(\mathrm{x})+10\mathrm{f}(\mathrm{x})-12\le 0$,

${\mathrm{f}}^2(\mathrm{x})-4\mathrm{f}(\mathrm{x})+3\ge 0$

${\mathrm{f}}^2(\mathrm{x})-6\mathrm{f}(\mathrm{x})+8\le 0$

If the equation to the tangent drawn from $(2,0)$ to the curve, $y=x^{2}f(\sin x)$ is of the form, $y=\alpha x-2\alpha ,\alpha \in R^{+}$, then the numerical value of $\frac{\alpha }{6}$ is,