Problems from Interpolation of Hermite

We know that: f(0)=3, f(0)=1, f(1)=2 and f(1)=2. Calculate the polynomial of Hermite that interpolates these points.

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Development:

In this case we have n+1=2 points, therefore the degree of the polynomial of Hermite will be 2n+1=3. We proceed as we explained, we write in a table the points repeating those in which we know the derivative:

0 3      
    f0=1    
0 3   1110=2  
    231=1   1+210=1
1 2   2+110=1  
    f1=2    
1 2      

Then, the polynomial is written in the same way, taking the first element of every column (starting from the second).

P3(x)=3+1(x0)2(x0)2+1(x0)2(x1)=3+x2x2+x3x2=x33x2+x+3

Solution:

P3(x)=x33x2+x+3

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