September 27th, 2011, 08:23 PM  #1 
Member Joined: Jun 2010 From: USA, Texas Posts: 85 Thanks: 0  Tangent Line Equation
Alright, I've been able to find the slope of a tangent line at the given points, and find the derivative by limit process, but I don't know how to "find an equation of the tangent line to the graph of 'f' at the given points." f(x) = x²+3x+4, (2,2) 
September 27th, 2011, 08:29 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Tangent Line Equation
Differentiating f wish respect to x, we find: Thus: So, we have the slope and the point, thus we may use the pointslope formula: 
September 27th, 2011, 08:44 PM  #3 
Member Joined: Jun 2010 From: USA, Texas Posts: 85 Thanks: 0  Re: Tangent Line Equation
So what exactly is the Tangent Line equation? y = x ? For example: f(x) = x²+3, (1,4) I know the derivative is f?(x) = 2x, but the answer I'm looking for is an Tangent Line equation at the points (1,4). The answer in the back of the book shows: y = 2x + 2. How did they arrive to that equation? And how do I correlate that with my original problem? 
September 27th, 2011, 08:51 PM  #4  
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Tangent Line Equation Quote:
Quote:
f'(1) = 2 So, we know the slope of the tangent line is 2 and it must pass through the given point (1,4). Using the pointslope formula, we get:  
September 27th, 2011, 09:01 PM  #5 
Member Joined: Jun 2010 From: USA, Texas Posts: 85 Thanks: 0  Re: Tangent Line Equation
Ah, that makes sense. Was forgetting what the pointslope formula was at first... Thanks! 
September 27th, 2011, 09:03 PM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Tangent Line Equation
Glad to assist! 
September 27th, 2011, 09:21 PM  #7 
Member Joined: Jun 2010 From: USA, Texas Posts: 85 Thanks: 0  Re: Tangent Line Equation
Okay, got a derivative question now. h(x) = (2x²  3x + 1) / (x) Since it's dividing x, how would I rewrite that into an equation I can just use the power rule? Or am I going to have to use some weird formula? :/ 
September 27th, 2011, 09:25 PM  #8 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Tangent Line Equation
No, (2x²  3x + 1)^(1) = 1/(2x²  3x + 1). What we are given is: 
September 27th, 2011, 09:30 PM  #9 
Member Joined: Jun 2010 From: USA, Texas Posts: 85 Thanks: 0  Re: Tangent Line Equation
Oh, I see... Tricky! So I'm getting to: h?(x) = 2 + 1?² So: 2 + (1/1²) => 2 + (1) = 1? 
September 27th, 2011, 09:36 PM  #10 
Member Joined: Aug 2009 Posts: 69 Thanks: 0  Re: Tangent Line Equation
(MarkFL might ninja post me but oh well) You forgot an important thing. so, if n=1, , NOT 1. Also, just a tip on the tangents: If you're not sure if something is a tangent line, and want to verify your work, type the graphs into wolfram alpha. http://www.wolframalpha.com/input/?i...2B3x%2B4%2C+x 

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equation, line, tangent 
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