Is there an infinitely differentiable function $f$ such that

  • $f(x)=0 \iff x=0$,
  • $f$ is infinitely differentiable
  • No derivative of $f$ is ever equal to zero.
  • 3
    $\begingroup$ Think about what you can do with the exponential function. $\endgroup$ – Git Gud Oct 10 '14 at 18:23

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

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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.