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Find equation for each tangent to curve y = 1 / (x-1) that has slope -1?


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#1 CrazCo

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Posted 27 October 2009 - 01:53 AM

lim f(x+h)-f(x) / h = -1 / (x-2)^2
h-> 0

-1 / (x-2)^2 = -1

I don't know what im doing help??
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#2 bob000555

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Posted 27 October 2009 - 02:09 AM

Use the quotient rule. Set the derivative equal to -1 to get the x value where the tanget is negative one. Then use y = mx+b to get the tangent line.
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#3 CrazCo

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Posted 27 October 2009 - 02:41 AM

thats what i did

x= 0,2

i just dont get the y = mx+b part
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#4 Cap'n Refsmmat

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Posted 27 October 2009 - 02:51 AM

Those are the x-coordinates of the points on the graph with slope -1. Then you find the y-coordinate using your equation y=\frac{1}{x-1} so you get the complete coordinate. You can stick the x and y into y=mx+b, using -1 as the slope, and find out the equations (solving for b).
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#5 bob000555

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Posted 27 October 2009 - 02:51 AM

Ok now get the derivative at x = 2 and x = 0 then find the value of the function at x = 2 and x =0 then find b such that y = mx + b remembering that the derivative gives the slope, M the original function gives Y and you already found X. There will be two sepret tangent lines and two seperate b's
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public String nim(int __, boolean ___) {_ -= _; while(Math.pow(2, _) <= __) { _++; }__ -= ___ ? sc.nextInt() : __ - Math.pow(2, _); ___ = !___; return __ != 1 ? nim(__, ___) : !___ ? "You win!" : "You lose!";}

#6 DJBruce

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Posted 27 October 2009 - 02:53 AM

If the slope of the tangent and the slope of the derivative are the same thing then you are looking for when the derivative equals -1.

If I where you I would rewrite the equation as follows:

\frac{1}{(x-1)}=(x-1)^{-1}

and then just solve it using the chain rule once you have the derivative remember a few things like:

\frac{dy}{dx}=m

y-y_{1}=m(x-x_{1})

So once you know when the derivative is equal to -1 you already have m and x. So all you need to know is what y is at the x points you find.
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#7 CrazCo

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Posted 27 October 2009 - 02:55 AM

of course i forgot to include the -1

damn i make sure i actually dont get something before i ask it then i realize how dumb my mistakes are.. lol
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