July 31st, 2012, 02:00 AM  #1 
Senior Member Joined: Jul 2012 Posts: 225 Thanks: 0  Rational function with parameters
hey, I have a really difficult question I've been tackling all morning. Appreciate any help you can give me. The slope of the tangent line to the function y=ax/(x^2bx+ at the point (3,3) is 1/10. find parameters a and b. Link to word documents so its easier to see the function (u guys gotta teach me how to be able to write equations on this forum) http://s137.photobucket.com/albums/q225 ... lculus.jpg What I've tried to do is, ive put 3 as my x and 3 as my y, and found the equation a=3b17 which is true. but when I derive this function to find either a or b, i find that b=8.57... and the answer in the book is b=9 and a=10 please help, show me the way to solve this. 
July 31st, 2012, 02:36 AM  #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: Rational function with parameters
We are given: hence: When we are told the derivative is equal to 1/10, hence: We are also given the point (3,3) on the curve, so we know: Substituting for a into the first equation yields: We discard the root as this does not satisfy the given conditions. Hence we are left with and so: 
July 31st, 2012, 02:46 AM  #3  
Senior Member Joined: Jul 2012 Posts: 225 Thanks: 0  Re: Rational function with parameters Quote:
 
July 31st, 2012, 02:51 AM  #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: Rational function with parameters
Let's look at the numerator, immediately after applying the quotient rule. I assume you are asking how this was simplified. Notice both terms have the common factor a, so let's factor that out: Now, remove the extraneous parentheses and distribute the : Collect like terms: 
July 31st, 2012, 02:54 AM  #5 
Senior Member Joined: Jul 2012 Posts: 225 Thanks: 0  Re: Rational function with parameters
ah common factor a that's right. Alright I get it. Thank you!

July 31st, 2012, 02:57 AM  #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: Rational function with parameters
Glad to help, and a belated welcome to the forum! 

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