Question

Show that f(x) = e^2x is increasing on R.

Answer 1

$$\begin{gathered} f\left(x\right)=e^{2x} \\ f\text{'}\left(x\right)=2e^{2x} \\ \mathrm{Now}, \\ x\in R \\ \mathrm{Since}t\mathrm{he\; value\; of}{\mathit{\text{e}}}^{2x}\text{is always positive for any real value of}\mathit{\text{x,}}{e}^{2x}>0. \\ \Rightarrow 2e^{2x}>0 \\ \Rightarrow f\text{'}\left(x\right)>0 \\ \text{So,}\mathit{\text{f}}\text{(}\mathit{\text{x}})\text{is increasing on}R. \end{gathered}$$