Solution 2 (d).

Construct the Lagrange interpolation polynomial [Graphics:../Images/LagrangePolyMod_gr_216.gif], of degree n = 5.  

[Graphics:../Images/LagrangePolyMod_gr_217.gif]


[Graphics:../Images/LagrangePolyMod_gr_218.gif]
[Graphics:../Images/LagrangePolyMod_gr_219.gif]

[Graphics:../Images/LagrangePolyMod_gr_220.gif]

Now graph the function and polynomial, and interpolation nodes.

[Graphics:../Images/LagrangePolyMod_gr_221.gif]

[Graphics:../Images/LagrangePolyMod_gr_222.gif]

[Graphics:../Images/LagrangePolyMod_gr_223.gif]
[Graphics:../Images/LagrangePolyMod_gr_224.gif]
[Graphics:../Images/LagrangePolyMod_gr_225.gif]

[Graphics:../Images/LagrangePolyMod_gr_226.gif]


[Graphics:../Images/LagrangePolyMod_gr_227.gif]

[Graphics:../Images/LagrangePolyMod_gr_228.gif]

[Graphics:../Images/LagrangePolyMod_gr_229.gif]
[Graphics:../Images/LagrangePolyMod_gr_230.gif]

[Graphics:../Images/LagrangePolyMod_gr_231.gif]

[Graphics:../Images/LagrangePolyMod_gr_232.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004