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

Question

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

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Answer

Given: $f\left( x \right) = {e^{2x}}$

$\therefore f'\left( x \right) = {e^{2x}}\frac{d}{{dx}}(2x) = {e^{2x}}\left( 2 \right) = 2{e^{2x}} > 0$ i.e., positive for all $x \in R$

Therefore, f(x) is strictly increasing on R.

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