The discussion focuses on the properties of the curves defined by the equations y=(4/x)+2 and y=ax^2+bx+c. Key findings include that both curves intersect at the point (2, 4) and share a common tangent line at this point. Additionally, both curves pass through the point (1, 6), leading to a system of equations that can be solved for the coefficients a, b, and c in the quadratic equation.
PREREQUISITESStudents studying calculus, mathematics educators, and anyone interested in the analysis of curves and their intersections in algebra and calculus.
their graphs both pass through (2, y). If x= 2 and y= (4/x)+ 2, what is y?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
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.b)there is a common tangent line at x=2
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.c)both curves pass through point (1,6)
You are welcome.thanks for help.