Suppose you want to compute the fifth root of 6 by solving the equation $$f(x) = x^5 - 6 = 0\quad(*)$$ using Newton's method. Newton's method starts with an initial approximation $x_0$ and then computes a sequence of approximations $x_1$, $x_2$, $x_3$, $\ldots$ via the formula $$x_{k+1} = g(x_k), \quad k = 0,1,2,\ldots$$ where $$g(x) = x - \frac{f(x)}{f'(x)}.$$ For the function defined above in $(*)$, $g(x) =$ .
Letting $$x_0= 1$$ you obtain
$x_1$ = ,
$x_2$ = , and
$x_3$ = .