$$ \text { The rate of change of the volume of a sphere with respect to its surface area } \mathrm{S} \text { is } $$

The turning point of the function $$y=\frac{a x-b}{(x-1)(x-4)}$$ at the point $$P(2,-1)$$ is

The side of a cube is equal to the diameter of a sphere. If the side and radius increase at the same rate then the ratio of the increase of their surface area is

What is the nature of the function $$f(x)=x^3-3 x^2+4 x$$ on real numbers?