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Re: DSolving(?) for a given tangent


f[x_] := E^(0.22 x)

Off[Solve::ifun];
pt = {x, f[x]} /. Solve[f'[x] == 1, x]

{{6.882398784680798, 
     4.545454545454546}}

Plot[f[x], {x, 4, 10}, 
 Epilog -> {Red, AbsolutePointSize[3], Point[pt]}, 
 AspectRatio -> Automatic]


Bob Hanlon

---- AngleWyrm <anglewyrm at yahoo.com> wrote: 
> Don't know for sure if this is the right function, so here's the scenario:
> 
> f[x_] := E^(0.22 x);
> Plot[f[x], {x, 6, 36}]
> 
> Which plots a nice escalating curve.
> 
> What I would like to know is: Where is the point {x,f[x]} that has a 
> 45-degree tangent line; ie where is this curve's balance point before it 
> really starts taking off?
> 
> 
> 



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