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Re: DSolving(?) for a given tangent


f[x_] := E^(0.22 x);
x45 = x /. FindRoot[f'[x] == 1, {x, 10}]

6.8824

or

f[x_] := E^(22 x/100);
x45 = x /. First@Quiet@Solve[f'[x] == 1, x]

50/11 Log[50/11]

and either way,

Plot[{f[x], f[x45] + x - x45}, {x, 0, 10}, Frame -> True,
  AspectRatio -> Automatic,
  Epilog -> {PointSize[0.02], Point[{x45, f@x45}],
    Text[{x45, f@x45}, {x45 + 1, f@x45 - 2/3}]}]

Bobby

On Thu, 20 Sep 2007 02:53:19 -0500, 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?
>
>
>
>



-- 

DrMajorBob at bigfoot.com


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