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Answer :
Final answer:
The derivative of the base polynomial L_1 at X0 as per Lagrange polynomial application in three-point formulas, assuming the difference between all x points is h, is -1/h.
Explanation:
In the case of Lagrange interpolation, the base polynomials are defined as:
L_i(x) = Π (for j ≠ i) [(x - x_j) / (x_i - x_j)], where i = 0, 1, 2, ..., n. Application of this formula for three-point formulas leads to three base polynomials L_0, L_1, and L_2
Deriving the base polynomial L_1, we substitute i as 1 in the formula and differentiate the result w.r.t x. The derivative of L_1 at X0 can be found as -1/h, assuming that the difference between all x points is h.
Therefore, none of the options given (3,2h,finh,4h) are correct. The exact value is -1/h.
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