The absolute minimum value of the function $f(x) = x^3 - 18x^2 + 96x$ for $x \in [0, 9]$ is:

If the function $f$ is given by $f(x)=x^3-3(a-2)x^2+3ax+7$,for some $a \in R$,is increasing in $(0,1]$ and decreasing in $[1,5)$,then a root of the equation $\frac{f(x)-14}{(x-1)^2}=0$ $(x \neq 1)$ is

Find the minimum value of $2x + 3y$ when $xy = 6$.

The maximum value of the function $f(x) = \frac{\log x}{x}, x > 0$ is

The ratio of the altitude of the cone of greatest volume which can be inscribed in a given sphere to the diameter of the sphere is:

If the function $f(x)=2 x^3-9 a x^2+12 a^2 x+1$,where $a > 0$,attains its local maximum and local minimum values at $p$ and $q$ respectively,such that $p^2=q$,then $f(3)$ is equal to: