Question
Determine a unique polynomial f(x) of degree such that
,
,
,
, where
.
Answer :
Word Count : 311
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Skip in 10
Let (f(x)) be a cubic polynomial: [ f(x) = a_0 + a_1(x-x_0) + a_2(x-x_0)^2 + a_3(x-x_0)^3 ] Then [ f'(x) = a_1 + 2a_2(x-x_0) + 3a_3(x-x_0)^2 ] Using the given conditions: 1. (f(x_0) = 1 \Rightarrow a_0 = 1) 2. (f'(x_0) = 2 \Rightarrow a_1 = 2) Next, at (x = x_1 = x_0 + h): [ f(x_1) = 1 + 2h
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