I ask the question, what is the value q of the exponential function q^x such that its derivative with respect to x is equal to itself?
Okay... dont just spout out the mindless answer "oh, q equals Euler's constant, 'e'"... not good enough.
'e' was originally defined as the base of an exponential function ( e^x ) such that it had a slope of 1 at x=0. Thats is what e is based on... its only coincidence that its derivative equals itself throughout its domain. That was proven as a consequence of its definition.
My proposition is, what if ∂/∂x e^x did not equal e^x... regardless of the fact that it has a slope of 1 at x=0.
How would mathematicians have determined (or proven to exist) that one special number, the base to an exponential function, whose derivative was equal to itself?
2007-11-07
15:06:12
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4 answers
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asked by
Anonymous