19. FINDING A MINIMUM VIA ITERATION - Consider f(x) = +22 x +3 a) Deduce an...

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19. FINDING A MINIMUM VIA ITERATION - Consider f(x) = +22 x +3 a) Deduce an equation that the position of the minimum satisfies. Assuming you have a calculator that can take 5th roots, rewrite equation in form: Im (...) 1/5 (0) = b) Start with some 0 < x < 1, iterate your equation at least 4 times. Find f(x)) at each iteration. c) By any means you like, find exact answer, and list errors in xm and fm after each iteration. d) Repeat starting from a different xm. Comment on the results. e) Try starting at xm = 1. What happens? How might you fix things? f) Plot the function, marking the iteration points. Do you notice a property the function has that guarantees a minimum and makes it relatively easy to find? 19. FINDING A MINIMUM VIA ITERATION - Consider f(x) = +22 x +3 a) Deduce an equation that the position of the minimum satisfies. Assuming you have a calculator that can take 5th roots, rewrite equation in form: Im (...) 1/5 (0) = b) Start with some 0 < x < 1, iterate your equation at least 4 times. Find f(x)) at each iteration. c) By any means you like, find exact answer, and list errors in xm and fm after each iteration. d) Repeat starting from a different xm. Comment on the results. e) Try starting at xm = 1. What happens? How might you fix things? f) Plot the function, marking the iteration points. Do you notice a property the function has that guarantees a minimum and makes it relatively easy to find?