May 27th, 2009, 07:36 AM  #1 
Newbie Joined: May 2009 Posts: 4 Thanks: 0  equation of a secant
Hello, I was wondering if I could ask for your help for this one questions. I have to determine the general equation of a secand from any point (a, f(a)) to the pont f (x) = 4^x where x = 2 and then i have to describe how i would use this to find the equation of the tangent at the point (2,f(2)). I'm really stuck and can't figure it out, I have m = (f(a)  f(16)/a  2) (x  2) + 16. But i know that this is way wrong, and i'm hoping one of you guys or girls could give me a nudge in the right direction. Thank you.

May 27th, 2009, 08:01 AM  #2 
Senior Member Joined: Jul 2008 Posts: 895 Thanks: 0  Re: equation of a secant
The tangent is the limiting secant as a point on the curve, (a,f(a)) approaches the general point (x,f(x)), or, specifically in this case, (2, f(2)) = (2,2^4), or (2,16). The general equation of the secant would be found as (y16)/(x2) = (f(a)16)/(a2) For tangency, a >2 in the limit, so you want to find lim[a>2] (f(a)16)/(a2), which is lim[a>2] (a^416)/(a2). Try factoring. You should wind up with (y16)/(x2) = 64 if I'm right. 
May 27th, 2009, 02:09 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,916 Thanks: 2199 
A couple of mistakes there methinks.

May 27th, 2009, 03:46 PM  #4  
Senior Member Joined: Jul 2008 Posts: 895 Thanks: 0  Re: Quote:
Oh, well, a bad hair day all around as the lawn tractor also went belly up. Things happen. How about removing a factor of 16, then using L'Hopital?  

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