(a) Fix real numbers a,b > 0 and plot the graph of f (x) = a 2 x 4 – 6abx 2 – 11b 2 for your…

(a) Fix real numbers a,b > 0 and plot the graph of f(x) = a2x4 − 6abx2 − 11b2 for your chosen values. Do not use a = 2, b = 1/2, since that case already appears in Example 1.15.

(b) Apply Newton’s method to find both the negative root and the positive root of f (x). Then find intervals of positive initial guesses [d1, d2], where d2 > d1, for which Newton’s Method:

(c) converges to the positive root,

(d) converges to the negative root,

(e) is defined, but does not converge to any root. Your intervals should not contain any initial guess where f’(x) = 0, at which Newton’s Method is not defined.

 

 

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