Consider the recursive sequence defined by:

N{t+1} = 25 + N{t}^3 for t = 0, 1, 2, 3,...

a) Provide the iterative function f for this recursive sequence. Use x as the variable.

b) Rewrite the equation f(x) = x to find the fixed points in the form g(x) = 0, where g(x) is a polynomial.

c) Use the Intermediate Value Theorem to find a closed interval [a, b] containing a fixed point. There are infinitely many valid answers to this question. Write the response in the form [a, b].

d) Use the Newton's method to estimate a fixed point by following these steps: Choose an initial approximation x0 within the interval you found in (c) and then compute four iterations of the Newton's method x1,x2,x3,x4. In the box, provide only your initial value x0 and your final value x4, in the format [x0,x4]. Provide your answers with a precision of at least three decimals.