can anyone help me with this math problem?

[DoNotDisturb]

i'm like totally stuck... any hints? don't give me the answer

Find tangent lines to curve x / (x+1) that pass through points (1,2).
At which points do these tangent lines touch the curve?

"given hints:"
1. use quotient rule
2. we have points, use point-slope formula
3. two answers

WHOOPS CHANGED the EQUATION

 

[ChOwDoWn]

take the derivative

 

[MacBaine]

take the derivative and you get that the tan line has a slope of -(1/2). you can do the rest.

Edit: Oops, it's -1/4

Edit: ok, let's try again with your new formula.

 

[DoNotDisturb]

well i took the derivative, i got x+1-x^2 / x^2+2x+1

do i substitute that for "m" in the pointslope formula, hence then i would have:

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

?

thats the farthest i've worked, but for some reason i'm stuck, i then speculated, therefore i'm posting to see if i made any errors.

 

[DoNotDisturb]

sorry, typo in the equation above, thats the equation i'm trying to work with, any mistake i've made?

 

[DoNotDisturb]

i need help, i've been trying to solve this all day.

 

[MacBaine]

Originally posted by: DoNotDisturb
i'm like totally stuck... any hints? don't give me the answer

Find tangent lines to curve x / (x+1) that pass through points (1,2).
At which points do these tangent lines touch the curve?

"given hints:"
1. use quotient rule
2. we have points, use point-slope formula
3. two answers

WHOOPS CHANGED the EQUATION

y = x(x+1)^-1

y^1 = x[-(x+1)^-2]+1(x+1)^-1
= m

use this to find an equation for the line. plug in 1 for X to get the slope.

= 1/4

then plug in x and y to find an equation. y-2=1/4(x-1)

y=(1/4)x+(7/4)

I dont know how you'd get 2 answers. I used multiplication rule instead of quotient... but this should give you a start.

 

[RossGr]

Here is my solution for this. I did not check my results, so you need to do that. I believe that this will get you were you need to go.

 

[hamburglar]

Originally posted by: RossGr
Here is my solution for this. I did not check my results, so you need to do that. I believe that this will get you were you need to go.

why do people put things in pdf format?

 

[RossGr]

Because most everybody has access to acrobat reader, while many may not have MS Word installed. It is just a nice universal format.

 

[DoNotDisturb]

anyone have the idea on how i get the points? do i just use my calc and find all the points of tangency?

 

[DoNotDisturb]

wait a sec, nm, of course you use the slope equation, thx guys.