I've tried to solve this problem for over 3 or 4 hours but I can't figure out how, please help me.
Ok so it's a curve ( parable? ) y = (ax - b) / ( 1 - x^2 )
You are supposed to solve what 'a' and 'b' should be if the curve goes through the point (-2,1) AND that the tangents* direction of that same point (-2,1) is 45 degrees ( so the tangents 'k' value should be 1, wich is 45 degrees ).
*I'm not sure but I might have the wrong name in English for 'tangent', but it is a line with the same 'k' value as the single point in the curve... if you know what I mean?
THE BELOW IS WHAT I'VE TRIED TO DO:
Ok, so we all know that to get the 'k' value of a point in a curve you must begin with taking the derivate of the curve, wich in this case would be:
MAOL s.43 : D f/g = ( gDf - fDg ) / ( g^2 )
#1. y' = ( ( 1-x^2 )*a - ( ax-b )*( 2x ) ) / ( 1 - x^4 )
and then you should put the derivate in a function of the x value, something like: y'(x) = ... , wich would in this case be: y'(-2) = ... .
so we take that y'(-2) = ... and equal it to 1, because that's the 'k' value we had to have for that point.
and thus we should get an equation with both 2 unknown variables, 'a' and 'b' , in wich we should somehow figure out what they should be to get this to work... wich is where I fail.
The answer for this problem is that 'a' and 'b' both = 1.
I've tried to do the countings myself etc but I can't come up with it...
Could someone please help me!?
And could someone clarify why I got an Infraction for spamming Advertisements in this post?? As far as I know I havn't adversided anything!
but it still leaves 2 unknown variables in the equation.
I cleaned up the equations and I got it to be:
so I put that equal to 1, wich was the needed angle ( k value ) of the point on the curve:
and here is where i'm stuck then...
I get etc, wich doesn't really help at all now does it?
so, where should I continue from here?
Once again, the solution to the problem is that 'a' and 'b' should both equal 1, but I have problems in getting there myself , help is much appreciated!
Ahh, now I've got it!
I take the first equation:
put in the point it should be on (-2,1)
wich makes it:
or , wichever you want.
As I said, I take the first equation and compare it to the result I got in the last post:
Then I take both of them and compare them:
I'll use the addition method so I take #1. times (-4) and I get:
then I kill the b's and I'm left with:
wich then is added to become:
and then I just put that a = 1 into for instance here:
Voila, thanks for all the help guys