Re: DSolving(?) for a given tangent

*To*: mathgroup at smc.vnet.net*Subject*: [mg81394] Re: DSolving(?) for a given tangent*From*: Adriano Pascoletti <adriano.pascoletti at gmail.com>*Date*: Sat, 22 Sep 2007 03:20:03 -0400 (EDT)*References*: <fct9c4$r6e$1@smc.vnet.net>

On Sep 20, 10:01 am, "AngleWyrm" <anglew... 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? In[2]:= f[x_] := E^(0.22*x); In[3]:= {x, f[x]} /. First[Quiet[Solve[D[f[x], x] == 45*Degree, x]]] Out[3]= {6.882398784680798, 4.545454545454546} Quiet suppresses the warning message: Solve::ifun:Inverse functions are being \ used by Solve, so some solutions may not be found; use Reduce for \ complete solution information. >> This verifies the result In[4]:= D[f[x], x]/Degree /. First[Quiet[Solve[D[f[x], x] == 45*Degree, x]]] Out[4]= 45. Adriano Pascoletti