GATE 2025 MT – Question 65
Two consecutive Newton–Raphson estimates of a root of $f(x)$ are $x_i=8.5$ and $x_{i+1}=13.5$, with $f(x_i)=15$. The first derivative $f\prime(x_i)$ is ______ (in integer).
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Correct answer: -3 to -3
Explanation
Newton–Raphson uses $x_{i+1}=x_i-f(x_i)/f\prime(x_i)$.
Substituting gives $13.5=8.5-15/f\prime(x_i)$, so $5=-15/f\prime(x_i)$. Therefore $f\prime(x_i)=\boxed{-3}$.