Solution 2 (c).

Construct the Lagrange interpolation polynomial [Graphics:../Images/LagrangePolyMod_gr_199.gif], of degree n = 4.  

[Graphics:../Images/LagrangePolyMod_gr_200.gif]


[Graphics:../Images/LagrangePolyMod_gr_201.gif]
[Graphics:../Images/LagrangePolyMod_gr_202.gif]

[Graphics:../Images/LagrangePolyMod_gr_203.gif]

Now graph the function and polynomial, and interpolation nodes.

[Graphics:../Images/LagrangePolyMod_gr_204.gif]

[Graphics:../Images/LagrangePolyMod_gr_205.gif]

[Graphics:../Images/LagrangePolyMod_gr_206.gif]
[Graphics:../Images/LagrangePolyMod_gr_207.gif]
[Graphics:../Images/LagrangePolyMod_gr_208.gif]

[Graphics:../Images/LagrangePolyMod_gr_209.gif]


[Graphics:../Images/LagrangePolyMod_gr_210.gif]

[Graphics:../Images/LagrangePolyMod_gr_211.gif]

[Graphics:../Images/LagrangePolyMod_gr_212.gif]
[Graphics:../Images/LagrangePolyMod_gr_213.gif]
[Graphics:../Images/LagrangePolyMod_gr_214.gif]

[Graphics:../Images/LagrangePolyMod_gr_215.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004