Re: DSolving(?) for a given tangent

• To: mathgroup at smc.vnet.net
• Subject: [mg81394] Re: DSolving(?) for a given tangent
• 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.