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

A manufacturer produces $x$ items per week at a total cost of ₹ $\left(x^2+78 x+2500\right)$. The price per unit is given by $8 x=600-\mathrm{p}$ where ' p ' is the price of each unit. Then the maximum profit obtained is