• Support PF! Buy your school textbooks, materials and every day products Here!

Tangent lines

  • Thread starter davedave
  • Start date
  • #1
50
0
Can someone help me with this problem?

Consider the curve defined by y=x/(x+1). (1,2) is a point NOT on the curve.
Find the equations of the two tangent lines to the curve passing through the point
(1,2).
 

Answers and Replies

  • #2
djeitnstine
Gold Member
614
0
There are some ways to attack this problem but my first instinct is to sketch or print the graph then mark the point (1,2) then take a ruler and carefully draw the tangent lines touching one point on each side of the graph. Then take the derivative around those points and use the formula of a line (y=mx+c) and check to see if the gradients run through the points.

This is perhaps tedious to say the least but I don't know how else to tackle the problem without any more information.

btw winplot should help with this.
 
  • #3
tiny-tim
Science Advisor
Homework Helper
25,832
249
hihi davedave! :smile:

Write y = ax + b for a typical line.

What is the restriction on a and b for it to pass through (1,2)?

Now find the equation for the points of intersection of that line with y=x/(x+1).

That should be a quadratic equation.

What is the condition for that equation to have two equal roots? :smile:
 

Related Threads for: Tangent lines

  • Last Post
Replies
6
Views
575
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
726
  • Last Post
Replies
3
Views
1K
Top