Exercise Solution 2.17

Exercise Solution 2.17

We seek to fit a cubic polynomial on the interval [0, 2] and another cubic polynomial on the interval [2, 4]. These take forms:



These must satisfy conditions [2.113] to [2.116]. The first condition requires that





The second condition requires


The third condition requires


and the fourth condition requires



We have eight equations in eight unknowns. These can be expressed as


which we solve to obtain


Our two polynomials are



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