Re: DSolving(?) for a given tangent

*To*: mathgroup at smc.vnet.net*Subject*: [mg81385] Re: [mg81358] DSolving(?) for a given tangent*From*: DrMajorBob <drmajorbob at bigfoot.com>*Date*: Fri, 21 Sep 2007 03:10:51 -0400 (EDT)*References*: <29733598.1190315398568.JavaMail.root@m35>*Reply-to*: drmajorbob at bigfoot.com

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