I think I know how to do this I just want to make sure. This is the question: "Find the points on the curve y=(x-1)/(x+2) whose tangents are parallel to the line y=3x+7. What is throwing me off is the parallel line. But here's what I think I do: 1.) I find the derivative of y=(x-1)/(x+2) which would be 1. Then I'm not sure where to go from there. Not looking for a solution to the problem but more of an outline of how I would approach similar problems of this nature.
Thanks
2006-09-16 11:01:55 · 3 answers · asked by wyndidancer 1 in Education & Reference ➔ Higher Education (University +)
It says I should give coordinates of the points and the equations of the tangents. I remember the y-y1=m(x-x1) is this what i use and where do I get the points - normally they are given to me.
2006-09-16 11:13:44 · update #1
Ok I have 3/(x^2 +2x+4) for the derivative of the first question and the derivative of the parallel line is 3
2006-09-16 11:17:28 · update #2
I'm not sure where to go now I tried solving for x from the above equation and I can't get an answer: it doesn't factor and it comes out to be a complex number via the quadratic equation. any help is appreciated
2006-09-16 11:55:38 · update #3
This is the answer I got. Is it right?
y=3x+13 (-3,4)
y=3x+1 (-1,-2)
2006-09-16 12:27:48 · update #4
The line has a slope of 3.
You need to take the derivative of (x-1)/(x+2) using the quotient rule. Note -- you did this wrong.
You now need to ask "When does this derivative equal three?"
This derivative is:
[(x+2)*1 - (x-1)*1]/(x+2)^2
This simplifies to:
3/(x+2)^2 = 3/(x^2+4x+4)
When does this equal three? You can solve for it directly -- ot notice that it is three when the bottom is one.
x^2 + 4x +4 = 1
x^2 + 4x +3 = 0
(x+3)*(x+1) = 0
the answer is when x = -3 or when x = -1
2006-09-16 12:05:10 · answer #1 · answered by Ranto 7 · 0⤊ 0⤋
first of all you got the derivative wrong for the curve in question. use the quotient rule to get correct answer. once you get the correct derivative, you set the derivative equal to the derivative of the line you want it to be parallel to and solve for x. once you have the x values just plug them into the original curve equation to get the y values. for a detailed explanation of how to find the derivative of the original curve go to the website below and just type in the equation. it not only gives the answer but gives step by step instructions.
2006-09-16 18:13:35 · answer #2 · answered by Matty G 2 · 0⤊ 0⤋
Wow, that's an awesome site Matty G! Thanks!
2006-09-16 18:22:04 · answer #3 · answered by nobodytoldme76 1 · 0⤊ 0⤋