**Unformatted text preview: **n such that there is a ﬁxed point of f in the interval [ n,n + 1) = { x ∈ IR : n ≤ x < n + 1 } . The number of times your algorithm calls the function f should be O (log | f (0) | ). Your pseudocode should include pre- and post-conditions. If you use a loop, you should also include a loop invariant in the pseudocode that you can use for part (c), below. (d) Prove that the algorithm given in part (b) is correct. Note: you do not have to prove that your algorithm calls f O (log | f (0) | ) times, but it should be true in order for your algorithm to get full marks. Example: The graph below shows the strictly decreasing function f ( x ) = (7-x ) 3 30 . It has a ﬁxed point between 2 and 3, so if your algorithm is run with this function f , it should output 2. 1...

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- Winter '16
- Calculus, Algorithms, Continuous function, strictly decreasing function