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

[linuxux]

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.

 

[berkeman]

-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?

 

[HallsofIvy]

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.