Proving x1 + x2 = -2 for Parallel Tangents to f(x) = 1/(x+1)

  • Thread starter rshalloo
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In summary, the problem involves finding the value of x1 + x2 if the tangents to the curve at x = x1 and x = x2 are parallel and x1 is not equal to x2. To solve this, we use the fact that if the tangent lines are parallel, their slopes are equal, and set f'(x1) equal to f'(x2). From there, we solve for x1 + x2 by manipulating the equation and taking into account that x1 is not equal to x2.
  • #1
rshalloo
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Homework Statement



f(x) = 1/(x+1)

If tangents to curve at x=x1 and x=x2 are parrallel and if x1 is not equal to x2
show that x1 + x2 = -2

The Attempt at a Solution



Well i found my equations for the asymptotes
Horizontal: x=0
Vertical: x= -1

and then i would say that if they were parrallel that the slopes are equal and therefore at the point x1 and the point x2 the slopes are equal

f1(x) = -1/(x+1)2

If i sub in x1 and x2, they will be equal and the question says they arent?

Can anyone help me please?
 
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  • #2


rshalloo said:

Homework Statement



f(x) = 1/(x+1)

If tangents to curve at x=x1 and x=x2 are parrallel and if x1 is not equal to x2
show that x1 + x2 = -2

The Attempt at a Solution



Well i found my equations for the asymptotes
Horizontal: x=0
Vertical: x= -1

and then i would say that if they were parrallel that the slopes are equal and therefore at the point x1 and the point x2 the slopes are equal

f1(x) = -1/(x+1)2

If i sub in x1 and x2, they will be equal and the question says they arent?

Can anyone help me please?
Your title is misleading - this problem doesn't have anything to do with asymptotes of either kind.

You are give that the tangent lines are parallel at x = x1 and x = x2, so f'(x1) = f'(x2). This means that -1/(x1 + 1)2 = -1/(x2 + 1)2. Solve that equation, keeping in mind that x1 [itex]\neq[/itex] x2, and that if a2 = b2 ==> a = b or a = -b.
 
  • #3


Mark44 said:
Your title is misleading - this problem doesn't have anything to do with asymptotes of either kind.
QUOTE]

Sorry about that it was just a part of a question with asymptotes and i asumed it was something to do with asymptotes :S thanks for the help
 

What is an asymptote in a math problem?

An asymptote in a math problem is a line that the graph of a function approaches but never touches. It can be either a vertical or horizontal line.

How do you find the asymptotes of a function?

To find the asymptotes of a function, you can use the following steps:
1. Simplify the function and put it in standard form.
2. Set the denominator equal to zero and solve for x. These values will be the vertical asymptotes.
3. Find the limit of the function as x approaches the values found in step 2. If the limit is infinite, there is a vertical asymptote.
4. If the limit is not infinite, check for any horizontal asymptotes by finding the limit of the function as x approaches infinity. If the limit exists, it will be the equation of the horizontal asymptote.

Can a function have more than one asymptote?

Yes, a function can have multiple asymptotes. It can have both vertical and horizontal asymptotes, and it is also possible for a function to have more than one of each type of asymptote.

Are asymptotes important in real-world applications?

Yes, asymptotes have real-world applications in fields such as engineering, physics, and economics. For example, in finance, asymptotes can represent the maximum or minimum values in a graph, which can help in decision making. In physics, asymptotes can represent the limits of a system, such as the maximum velocity of an object.

How do you graph a function with an asymptote?

To graph a function with an asymptote, follow these steps:
1. Find the asymptotes of the function using the methods mentioned in the second question.
2. Plot the asymptotes as dashed lines on the graph.
3. Plot points on either side of the asymptotes and connect them with a smooth curve.
4. Check the behavior of the graph near the asymptotes and make the necessary adjustments, such as using open or closed circles.

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