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Newton's Method Animation
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The following is an animation which demonstrates Newton's Method for finding the root of a function. In this example the function unders consideration is f(x)=7x^3 +x -6. The initial guess is x0=5.
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x[0] = 5., f[x[0]] = 874., f'[x[0]] = 526.
x[1] = 3.33840304, f[x[1]] = 257.782394, f'[x[1]] = 235.043632
x[2] = 2.24166031, f[x[2]] = 75.0927047, f'[x[2]] = 106.52586
x[3] = 1.53673567, f[x[3]] = 20.9403524, f'[x[3]] = 50.5926866
x[4] = 1.12283489, f[x[4]] = 5.03219776, f'[x[4]] = 27.4759218
x[5] = 0.939685516, f[x[5]] = 0.74794003, f'[x[5]] = 
 
  19.5431863
x[6] = 0.901414375, f[x[6]] = 0.0285107294, f'[x[6]] = 
 
  18.0635054
^*)