What are the properties of curves with equations y=(4/x)+2 and y=ax^2+bx+c?

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In summary, the curves with equations y=(4/x)+2 and y=ax^2+bx+c have a common point at x=2, a common tangent line at x=2, and both pass through point (1,6). To find the values of a, b, and c, plug in x=2 and (1,6) and solve the resulting equations. Differentiate both equations and set them equal to each other to get a second equation, and plug in x=1 and solve for a third equation.
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linuxux
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Homework Statement


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.
 
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  • #2
-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?
 
  • #3
linuxux said:

Homework Statement


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
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.

b)there is a common tangent line at x=2
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.

c)both curves pass through point (1,6)
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.

thanks for help.
You are welcome.
 

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