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MathGroup Archive 2007

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Re: DSolving(?) for a given tangent

  • To: mathgroup at smc.vnet.net
  • Subject: [mg81390] Re: DSolving(?) for a given tangent
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Fri, 21 Sep 2007 03:13:28 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <fct9c4$r6e$1@smc.vnet.net>

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 
(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[1]:=
f[x_] := E^(0.22 x);
Plot[f[x], {x, 6, 36}]
sol = NSolve[f'[x] == Pi/4, x]
x /. sol[[1]]

Out[3]= {{x -> 5.78438}}

Out[4]= 5.78438

HTH,
-- 
Jean-Marc


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