Expert: Paul Klarreich - 2/1/2009

Question
QUESTION: Find the points on the curve y=2/3x-2 where the tangent is parallel to the line
y=    3
   -   x  -1
     2



ANSWER: Questioner:   Michael
Category:  Calculus
Private:  No
 
Subject:  Tangent Help Please
Question:  Find the points on the curve y=2/3x-2 where the tangent is parallel to the line
y=    3
  -   x  -1
    2

......................
Hi Michael,

Sorry but your question did not come through in a readable fashion.  I THINK you meant:

      2
y = ------
   3x - 2

and  y = -3x/2 - 1.

If so, here is what you do:

1) The LINE has a slope of - 3/2

2) The curve y = f(x) has a derivative.  Find dy/dx.  Whatever you get, set it equal to -3/2 and solve for x.

3) Take the solution(s).  Substitute each into f(x) to get a corresponding y.

Now you have your points.


---------- FOLLOW-UP ----------

QUESTION: Yes yes that i was what I meant. I am not able to find the dervivative of the Curve can you please show me the solution to that?

Answer
Questioner:   Michael
Category:  Calculus
Private:  No
 
Subject:  Slope of the Tangent
Question:  QUESTION: Find the points on the curve y=2/3x-2 where the tangent is parallel to the line
y=    3
  -   x  -1
    2



ANSWER: Questioner:   Michael
Category:  Calculus
Private:  No

Subject:  Tangent Help Please
Question:  Find the points on the curve y=2/3x-2 where the tangent is parallel to the line
y=    3
 -   x  -1
   2

......................
Hi Michael,

Sorry but your question did not come through in a readable fashion.  I THINK you meant:

     2
y = ------
  3x - 2

and  y = -3x/2 - 1.

If so, here is what you do:

1) The LINE has a slope of - 3/2

2) The curve y = f(x) has a derivative.  Find dy/dx.  Whatever you get, set it equal to -3/2 and solve for x.

3) Take the solution(s).  Substitute each into f(x) to get a corresponding y.

Now you have your points.


---------- FOLLOW-UP ----------

QUESTION: Yes yes that i was what I meant. I am not able to find the dervivative of the Curve can you please show me the solution to that?
 
---------------------------------------

Since y = 2(3x - 2)^-1, you just use the Power(Chain) Rule, with  u = 3x - 2


y' = - 2u^-2(du/dx)
     -2(3)
= -----------
  (3x - 2)^2

etc.

(Or use the quotient rule.)