Solution 2 (b).

Construct the Lagrange interpolation polynomial [Graphics:../Images/LagrangePolyMod_gr_182.gif], of degree n = 3.  

[Graphics:../Images/LagrangePolyMod_gr_183.gif]


[Graphics:../Images/LagrangePolyMod_gr_184.gif]
[Graphics:../Images/LagrangePolyMod_gr_185.gif]

[Graphics:../Images/LagrangePolyMod_gr_186.gif]

Now graph the function and polynomial, and interpolation nodes.

[Graphics:../Images/LagrangePolyMod_gr_187.gif]

[Graphics:../Images/LagrangePolyMod_gr_188.gif]

[Graphics:../Images/LagrangePolyMod_gr_189.gif]
[Graphics:../Images/LagrangePolyMod_gr_190.gif]
[Graphics:../Images/LagrangePolyMod_gr_191.gif]

[Graphics:../Images/LagrangePolyMod_gr_192.gif]


[Graphics:../Images/LagrangePolyMod_gr_193.gif]

[Graphics:../Images/LagrangePolyMod_gr_194.gif]

[Graphics:../Images/LagrangePolyMod_gr_195.gif]
[Graphics:../Images/LagrangePolyMod_gr_196.gif]

[Graphics:../Images/LagrangePolyMod_gr_197.gif]

[Graphics:../Images/LagrangePolyMod_gr_198.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004