       Re: DSolving(?) for a given tangent

• To: mathgroup at smc.vnet.net
• Subject: [mg81398] Re: DSolving(?) for a given tangent
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Sat, 22 Sep 2007 03:22:08 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <fct9c4\$r6e\$1@smc.vnet.net> <fcvrjh\$7ur\$1@smc.vnet.net>

```Jean-Marc Gulliet wrote:
> AngleWyrm 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?
>
> So what you are looking for is the value of x for which f'[x] == Pi/4

simultaneously burnt some of my neurons and nothing surprise me when I
wrote this "answer". The right thing we are looking for is f'[x] == 1.

> (i.e. the slope of the tangent at x is 45 degrees but it must be
> expressed in radians rather than in degrees). The solution can be found
> by solving the equation f'[x] == Pi/4 for x; to do so one can use Solve
> or Reduce for an analytic solution (which implies exact coefficients
> such as 22/100 rather than 0.22) or NSolve or FindRoot for an numerical
> solution. For instance,
>
> In:=
> f[x_] := E^(0.22 x);
> Plot[f[x], {x, 6, 36}]
> sol = NSolve[f'[x] == Pi/4, x]
> x /. sol[]
>
> Out= {{x -> 5.78438}}
>
> Out= 5.78438

The following fixed code yields the correct result.

In:= f[x_] := E^(0.22 x);
Plot[f[x], {x, 6, 36}]
sol = NSolve[f'[x] == 1, x]
x /. sol[]
FindRoot[f'[x] == 1, {x, 6}]

Out= {{x -> 6.8824}}

Out= 6.8824

Out= {x -> 6.8824}

Again, sorry for the confusion.
Regards,
--
Jean-Marc

```

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