GATE 2023 MA – Question 28
Let p(x)=x³−2x+2. The polynomial q of degree at most 4 interpolates q(−2)=p(−2),q(−1)=p(−1),q(0)=2.5,q(1)=p(1),q(3)=p(3). Find q⁽⁴⁾(0).
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Correct answer: 2 to 2
Explanation
Only the datum at 0 differs from p, by 0.5. Its Lagrange basis is L₀=(x+2)(x+1)(x−1)(x−3)/6. Therefore q=p+L₀/2, whose leading coefficient is 1/12. The fourth derivative is 4!/12=**2**.