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Homework Help: Completely lost on this one.

  1. Apr 23, 2007 #1
    1. The problem statement, all variables and given/known data
    curves with equation y=(4/x)+2 and y=ax^2+bx+c have the following properties:
    a) there is a common point at x=2
    b)the is a common tangent line at x=2
    c)both curves pass through point (1,6)

    thanks for help.
     
  2. jcsd
  3. Apr 23, 2007 #2

    berkeman

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    Staff: Mentor

    -a- Plug x=2 into both. What happens?

    -b- Differentiate both and plug in x=2. What happens?

    -c- Plug in the x,y point given. What happens?
     
  4. Apr 23, 2007 #3

    HallsofIvy

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    Science Advisor

    their graphs both pass through (2, y). If x= 2 and y= (4/x)+ 2, what is y?
    Putting x= 2 and that value of y into y= ax^2+ bx+ c gives you one quation for a, b, c.

    So they have the same derivative at x= 2. What is the derivative of y= (4/x)+ 2 at x= 2? What is the derivative of y= ax^2+ bx+ c at x=2? Setting those equal gives you a second equation for a, b, c.

    Well, yes it true that y= (4/1)+2= 6. If x= 1 then y= a+ b+ c= 6 which is a third equation for a, b, c. Solve those 3 equations for a, b, c.

    You are welcome.
     
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