Exercise 6.2 Qn 3 Class 12 Mathematics NCERT

Question:

Show that the function given by $f(x)=e^{2x}$ is increasing on R

Answer:

here

\begin{array}{l}f(x)=e^{2x}\\ f^{\prime }(x)=2e^{2x}\\ \text{Now,}\\ x\in R\\ e^{2x}>0\text{ for all }x\in R\end{array}

(Because the exponential function $e^x$ is defined for all real numbers and always results in a positive value.)

Therefore the function is strictly increasing on R.