Re: DSolving(?) for a given tangent

• To: mathgroup at smc.vnet.net
• Subject: [mg82533] Re: DSolving(?) for a given tangent
• From: Peter Pein <petsie at dordos.net>
• Date: Wed, 24 Oct 2007 04:22:10 -0400 (EDT)
• References: <fct9c4\$r6e\$1@smc.vnet.net> <fd2fmv\$s0e\$1@smc.vnet.net> <ffhs2n\$5md\$1@smc.vnet.net>

```No, he accidentally used "invisibleTan[]" ;-)

Peter

Jerry schrieb:
> Sir, for some reason this does not work on my XP machine
> using V6. I get the correct answer if I use
>
> In[3]:= {x, f[x]} /. First[Quiet[Solve[D[f[x], x] == 1.0, x]]]
>
> This gives {6.8824, 4.54545} for output.
>
> I'm guessing your "Degree" is different from mine which is
> 0.0174533.
>
> Regards, Jerry
>
>> 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.
>>