The function arctan(x) has some unusual interactions with Newton's method. Verify the following properties for f(x)...

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The function arctan(x) has some unusual interactions with Newton's method. Verify the following properties for f(x) = arctan(17 x): (a) f has a simple root at x = 0 (b) f' exists at all real numbers (c) f is monotonically increasing (d) Newton's method does not converge for x0 = 1 Find the largest range [-d, d] on which Newton's method converges for f. The function arctan(x) has some unusual interactions with Newton's method. Verify the following properties for f(x) = arctan(17 x): (a) f has a simple root at x = 0 (b) f' exists at all real numbers (c) f is monotonically increasing (d) Newton's method does not converge for x0 = 1 Find the largest range [-d, d] on which Newton's method converges for f.