GATE 2024 MA – Question 33

Numerical Analysis · Interpolation · 1 mark · Numerical answer

P_f is the quadratic interpolant of f(x)=x²|x| at −1,0,1. Find sup on [−1,1] of |f−P_f|, to two decimals.

Show answer and explanation

Correct answer: 0.14 to 0.16

Explanation

Values 1,0,1 give P_f=x². Set t=|x|∈[0,1]; error is t²−t³. Derivative 2t−3t² vanishes at t=2/3, with maximum 4/27=0.148148. Rounded **0.15**.

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