Finding equation of derivative that is parallel to another line

[hachi_roku]

Homework Statement

find equations of the tangent lines to the curve
y= x-1/x+1


that are parallel to the line x-2y = 2

Homework Equations

The Attempt at a Solution

ok so i found the derivative, then set it equal to the slope (-1). then plugged x back into the original equation to get

y = -x + 41/14 and y= -x + 17/10


is this right? thanks in advance!

 

[gabbagabbahey]

Are you sure that the slope of x-2y=2 is -1? ;0)

 

[hachi_roku]

oops

 

[hachi_roku]

so the slope is 1/2...i plugg that in so my answer is now y = x-1. is this correct?

 

[gabbagabbahey]

Your slope is right now, but you should be getting two lines; and the one you have is incorrect. Let's star with your solutions for x from setting dy/dx=1/2...what do you get for those?

 

[hachi_roku]

from there, my solutions for x = x^2 + 2X + 1 = 4...then x^2 + 2x -3 = 0.

is my dy/dx wrong? i get 2/(x+1)^2

 

[gabbagabbahey]

your dy/dx is right; but what are the solutions to x^2+2x-3=0?

 

[hachi_roku]

my solutions are x = -2+or-4/2. from there one equation i get is y= x/2+7/2 and the other is y=x/2-1/2

 

[gabbagabbahey]

how do you get x=-2 or -4/2?! (-2)^2+2(-2)-3=-3 not zero...did you try factoring the quadratic?

 

[hachi_roku]

i meant -2+or-4 all over 2.

 

[gabbagabbahey]

Either way its still incorrect; x^2+2x-3=(x+3)(x-1) so x=1 or x=-3.

 

[hachi_roku]

ya tahts what i got...i was tryin to say that x = -2+-4/2 which equaled 1,-3. my mistake.

when i plug them in and put in the form i get y=x/2+7/2 and y= x/2-1/2. thanks for your help btw

 

[gabbagabbahey]

Okay, looks good. :0)