Question: Sometimes Newton's method fails no matter what initial value x 0 is chosen (unless you are lucky enough to choose the root itself). Let f(x)
Sometimes Newton's method fails no matter what initial value x0 is chosen (unless you are lucky enough to choose the root itself). Let f(x) = 3√x and choose x0 arbitrarily (x0 ≠ 0).
a. Show that xn+1 = −2xn for n = 0, 1, 2, ... so that the successive guesses generated by Newton's method are x0, −2x0, 4x0,....
b. Use your graphing utility to graph f(x), and use an appropriate utility to draw the tangent lines to the graph of y = f(x) at the points that correspond to x0, −2x0, 4x0,... Why do these numbers fail to estimate a root of f(x) = 0?
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a b To use the graphing utility to graph f and to draw the t... View full answer
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