Illustrate using a graph, the fixed point method for solving the equation x = g(x) in each of the following cases: g′(α) −1

Let g be a continuous function on an interval [a, b] and let α be a fixed point of g. We further suppose that g′ is continuous on [a, b]. 1. Illustrate using a graph, the fixed point method for solving the equation x = g(x) in each of the following cases: g′(α) < −1;−1 < g′(α) < 0;0 ≤ g′(α) < 1;g′(α) > 1

2. Propose a matlab code for each of the fourth previous cases.

[Adam]

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