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I know that the upper bound of an exponential function is given by $e^{-x} \leq \frac{1}{1+x}$, but how do I find the upper bound of the difference of exponential functions?

For example, what is the upper bound of $e^{-a} - e^{-b}$ ?

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You can use the Mean Value Theorem $$\frac{f(b)-f(a)}{b-a}=f'(\xi)$$ with $\xi \in [a,b]$

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  • $\begingroup$ Thank you very much. $\endgroup$
    – King008
    Aug 9, 2019 at 2:25

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