Math Problem Statement
Minimize the function 𝑓(𝑥) = 𝑥 3 − 6𝑥 2 + 11𝑥 − 6 using the Fibonacci search method over the interval [1, 4]. Perform the search until the uncertainty range is reduced to less than 0.3.
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Optimization
Numerical Methods
Formulas
Fibonacci search method ratio: (F_n / F_{n+2})
Cubic function: f(x) = x^3 - 6x^2 + 11x - 6
Theorems
Fibonacci Search Algorithm
Uncertainty Reduction in Optimization
Suitable Grade Level
Undergraduate Level (Mathematics or Engineering)
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