The radius of the base of a cone is increasing at the rate $3 \mathrm{~cm} /$ minute and the altitude is decreasing at the rate $4 \mathrm{~cm} /$ minute . The rate at which the lateral surface area is changing, when the radius is 7 cm and altitude is 24 cm is

The function f defined by $\mathrm{f}(x)=(x+2) \mathrm{e}^{-x}$ is

If the function $\mathrm{f}(x)=x(x+3) \mathrm{e}^{-\frac{x}{2}}$ satisfies all the conditions of Rolle's theorem in $[-3,0]$, then c is