       Re: DSolving(?) for a given tangent

• To: mathgroup at smc.vnet.net
• Subject: [mg81388] Re: [mg81358] DSolving(?) for a given tangent
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Fri, 21 Sep 2007 03:12:26 -0400 (EDT)
• Reply-to: hanlonr at cox.net

```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, 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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