Show that the function given by f(x) = e^ 2x is strictly increasi… - Vidyadip

Question

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

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Answer

Given: $f(x) = e^{2x}$
$\therefore\ \text{f} '(\text{x})=e^{2\text{x}}\frac{\text{d}}{\text{dx}}\ 2\text{x}=\text{e}^{2\text{x}}(2)=2\text{e}^{2\text{x}}>0$ i.e., positive for all $\text{x}\in \text{R}$
Therefore, f(x) is strictly increasing on R.

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