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November 6th, 2016, 08:54 PM  #1 
Newbie Joined: Nov 2016 From: United States Posts: 2 Thanks: 0  looking for an equation of a curve
While reading about Riemann, I came across a relation between random numbers and e. I am not sure if Riemann discovered the relation. This led to an empirically calculated curve that connects the points 0,1 and 1,e, in which the slope at x=0 is 1 and the slope at x=1 is 2. Has anyone seen such a curve and might there be a formula for it? Last edited by skipjack; November 7th, 2016 at 01:16 AM. 
November 6th, 2016, 09:18 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,203 Thanks: 1157 
$f(x) = x\left(\dfrac x 2 +1\right)$ satisfies $f^\prime(0)=1,~f^\prime(1)=1$ 
November 7th, 2016, 12:33 AM  #3 
Newbie Joined: Nov 2016 From: United States Posts: 2 Thanks: 0  sorry, I gave wrong boundary condition
I used Excel trendline and requested an exponential curve. it gave a curve almost identical to y=e^x. this means the slope at x=1 is e, not 2 as I stated before. So my question is answered. 

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