Word Count : 635

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To determine a unique polynomial \( f(x) \) of degree \(\leq 3\) that satisfies the given conditions, we proceed with the following steps: ### Step 1: Define the Polynomial A general cubic polynomial can be written as: \[ f(x) = ax^3 + bx^2 + cx + d \] where \( a, b, c, d \) are coefficients to be determined. ### Step 2: Apply the Given Conditions We are given: 1. \( f(x_0) = 1 \) 2. \( f'(x_0) = 2 \) 3. \( f(x_1) = 2 \) 4. \( f'(x_1) = 3 \) where \( x_1 = x_0 + h \). First, compute the ______ __________ ___ ______ ______ ________ ____ ___ ___ _______.
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