If $$f(x)=2x^3-15x^2-144x-7$$, then $$f(x)$$ is strictly decreasing in

The equation of tangent to the circle $$x^2+y^2=64$$ at the point $$\mathrm{P\left(\frac{2\pi}{3}\right)}$$ is

Water is being poured at the rate of 36 m$$^3$$/min. into a cylindrical vessel, whose circular base is of radius 3 m. Then the wate level in the cylinder is rising at the rate of

A wire of length 20 units is divided into two parts such that the product of one part and cube of the other part is maximum, then product of these parts is