The equation of the tangent to the curve $$y = 4x{e^x}$$ at $$\left( { - 1,{{ - 4} \over e}} \right)$$ is

The maximum volume of a right circular cylinder if the sum of its radius and height is 6 m is

The equation of the normal to the curve $2 x^2+y^2=12$ at the point $(2,2)$ is

The area of the square increases at the rate of $0.5 \mathrm{~cm}^2 / \mathrm{sec}$. The rate at which its perimeter is increasing when the side of the square is 10 cm long, is