Is there an infinitely differentiable function such that $f$ intersects the $x$ axis only at the origin and no derivative of $f$ is $0$?

Question

Is there an infinitely differentiable function $f$ such that

$\begingroup$ Think about what you can do with the exponential function. $\endgroup$ – Git Gud Oct 10 '14 at 18:23 — Git Gud, Oct 10 '14 at 18:23

Ri-Li · Accepted Answer · 2014-10-10 18:23:35Z

5

Consider the function $f:\Bbb R \to \Bbb R$ s.t $f(x)=e^x-1$.

answered Oct 10 '14 at 18:23

Ri-Li

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$\begingroup$ Precisely what I thought about when I saw the question. (+1) $\endgroup$ – robjohn♦ Oct 10 '14 at 19:03

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