Solution 2 (a).

Construct the Lagrange interpolation polynomial [Graphics:../Images/LagrangePolyMod_gr_165.gif],  of degree n = 2.  

[Graphics:../Images/LagrangePolyMod_gr_166.gif]

[Graphics:../Images/LagrangePolyMod_gr_167.gif]
[Graphics:../Images/LagrangePolyMod_gr_168.gif]

[Graphics:../Images/LagrangePolyMod_gr_169.gif]

Now graph the function and polynomial, and interpolation nodes.

[Graphics:../Images/LagrangePolyMod_gr_170.gif]

[Graphics:../Images/LagrangePolyMod_gr_171.gif]

[Graphics:../Images/LagrangePolyMod_gr_172.gif]
[Graphics:../Images/LagrangePolyMod_gr_173.gif]
[Graphics:../Images/LagrangePolyMod_gr_174.gif]

[Graphics:../Images/LagrangePolyMod_gr_175.gif]


[Graphics:../Images/LagrangePolyMod_gr_176.gif]

[Graphics:../Images/LagrangePolyMod_gr_177.gif]

[Graphics:../Images/LagrangePolyMod_gr_178.gif]
[Graphics:../Images/LagrangePolyMod_gr_179.gif]
[Graphics:../Images/LagrangePolyMod_gr_180.gif]

[Graphics:../Images/LagrangePolyMod_gr_181.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004