GATE 2022 MA – Question 44
A quadratic interpolant through (−1,f(−1)),(0,f(0)),(2,f(2)) approximates f′(0)=−(2/3)f(−1)+αf(0)+βf(2), for smooth f on (−3,3). Find 1/(αβ).
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Correct answer: (D) 12
Explanation
The Lagrange bases at 0 and 2 are L₀=−(x+1)(x−2)/2 and L₂=x(x+1)/6. Their derivatives at zero are α=1/2 and β=1/6. The −1 basis derivative is −2/3 as given. Thus 1/(αβ)=**12, D**.