Find the intervals in which $f\left(x\right)=(x+2)e^{-x}$ is increasing or decreasing?

Show that the function $\mathrm{f}$ given by $\mathrm{f}\left(\mathrm{x}\right)={10}^{\mathrm{x}}$ is increasing for all $\mathrm{x}$?

Prove that the following function is increasing on $\mathrm{ℝ}$: $\mathrm{f}\left(\mathrm{x}\right)=3{\mathrm{x}}^5+40{\mathrm{x}}^3+240\mathrm{x}$.

Prove that the following function is increasing on $\mathrm{ℝ}$: $\mathrm{f}\left(\mathrm{x}\right)=4{\mathrm{x}}^3-18{\mathrm{x}}^2+27\mathrm{x}-27$.