Re: DSolving(?) for a given tangent

• To: mathgroup at smc.vnet.net
• Subject: [mg81386] Re: DSolving(?) for a given tangent
• From: Bill Rowe <readnewsciv at sbcglobal.net>
• Date: Fri, 21 Sep 2007 03:11:22 -0400 (EDT)

```On 9/20/07 at 3:53 AM, anglewyrm at yahoo.com (AngleWyrm) wrote:

>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?

At that point, the slope of the function will be 1. So, simply
solve for the point where the derivative of the function is 1, i.e.,

In[6]:= FindRoot[D[f[x], x] == 1, {x, 5}]

Out[6]= {x->6.8824}
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