Item$8$

Item $8$

Develop a Python function to locate a minimum with the golden$-$section search. Rather than using the maximum iteration and equation$$ a$=(2)$xu$$xlxopt$$a$=2-$xu$-$xlxopt as stopping criteria, determine the number of iterations needed to attain the desired tolerance. Use the equation $(2)($xu$$xl$)(1)$n$=$Ea$2-$xu$-$xl$-1$n$=$Ea $.$

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Use the Python function to solve the following problem using desired absolute error$$a$=0\mathrm{.}0001.$

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f$($x$)=$x$2102$sin$($x$)$fx$=$x$210-2$sinx

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Use the golden$-$section within the interval from xl $=0$ to xu $=4.$

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The minimum of the function occurs at x $=.$

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The function value is $.$

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The relative error is $105.$

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The number of iterations needed to attain the desired tolerance is