So this is my graph enter image description here

I am aware that we can see its not a cubic spline because $p_1(x), 0≤x≤1$ is linear. But I wanted to prove it and got stuck.

From what I know, For it to be a natural cubic spline, the second derivatives of the endpoints needs to be 0. Endpoints are at x=0 and x=3. I set up my equations accordingly.

enter image description here

This is were I get stuck. I dont know what I should do next.


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