# Prove that $e^{x}$ is strictly increasing function on $R$.

Toolbox:
• (i) If $f'$ is positive on an open interval $I$. Then $f$ is strictly increasing on $I$
• (ii) If $f'$ is negative on an open interval $I$, then $f$ is strictly decreasing on $I$
Let $f(x)=e^x$ Which is defined and differentiable on $R$
$f'(x) =e^x >0$ for all $x\in R$
$\therefore e^x$ is strictly increasing on $R$