How would I go about proving that given
Then and must be exponential functions.
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Differentiate the first equation to get
And from there you should (probably) know how to solve it (since you're being asked this :P)
the problem here is that we don't know if is twice differentiable.
here's a way to proceed: we have then so where
on the other hand is easy to see that for whereat and as required.
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