Fine the root of the equation
f(x)=2x(1−x^2+x)ln(x)-x^2+1
in the interval [0, 1] by Newton’s method where x0=0.5... The problem I am getting is that when I calculate x1 = x0 - f(x)/f'(x), I get 0, but the root is at 0.32... ideas?

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Are you sure that's the right equation? That has no roots in the interval [0,1].

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