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July 31st, 2012, 02:00 AM   #1
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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^2-bx+ 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=3b-17 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.
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July 31st, 2012, 02:36 AM   #2
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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:

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July 31st, 2012, 02:46 AM   #3
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Re: Rational function with parameters

Quote:
Originally Posted by MarkFL
We are given:

hence:

please explain. Ok I know how to derive a rational function, but how did you get from the derivative to the right side of your equation, if you know what I mean.
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July 31st, 2012, 02:51 AM   #4
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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:

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July 31st, 2012, 02:54 AM   #5
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Re: Rational function with parameters

ah common factor a that's right. Alright I get it. Thank you!
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July 31st, 2012, 02:57 AM   #6
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Re: Rational function with parameters

Glad to help, and a belated welcome to the forum!
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