Answer to Question #177625 in Mechanical Engineering for Von Nikko

Question #177625

Determine the root of f(x)=x3-6x2+11x-6.1 using the Newton-Rapson Method(three iterations, xi=3.5)


1
Expert's answer
2021-04-12T01:53:12-0400

Given

"f(x)=x^3-6x^2+11x-6"

"f'(x)=3x^2-12x+11"

"x_0=3.5"

"x_{n+1}=x_n-\\dfrac{f(x_n)}{f'(x_n)}"




"\\def\\arraystretch{1.5}\n \\begin{array}{c:c:c:c:c}\n Step & x_0 & f(x_0) & x_1 & f(x_1) \\\\ \\hline\n 1 & 3.500000 & 1.875000 & 3.173913 & 0.443823 \\\\\n \\hdashline\n 2 & 3.173913 & 0.443823 & 3.032307 & 0.067779 \\\\\n \\hdashline\n 3 & 3.032307 & 0.067779 & 3.001456 & 0.002918 \\\\\n \\hdashline\n 4 & 3.001456 & 0.002918 & 3.000003 & 0.000006 \\\\\n\\end{array}"


Root is : "x=3.000003"



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