10. (a) The roots are sqrt(-c) and -sqrt(-c). |
(b) The graph of the Newton function for x^{2} - 1/2 |
(c) Newton's method takes any x > 0 to the root sqrt(1/2), and takes any x < 0 to the root -sqrt(1/2). |
(d) The graph of the Newton function for x^{2} - 3/2 |
(e) Newton's method takes any x < 0 to the root -sqrt(3/2). |
(f) The graph of the Newton function for x^{2} + 1/2 |
(g) Points appear to wander all over the place, being thrown from one side of 0 to the other. |
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